. 


A  TREATISE  ON 


LOG  I  C. 


OR, 


THE  LAWS  OF  PUJiE  THOUGHT; 

COMPRISING   BOTH 

THE    ARISTOTELIC    AND    HAMILTONIAN 
ANALYSES    OF   LOGICAL   FORMS, 

AND   SOME    CHAPTERS   OF 

APPLIED    LOGIC. 


By  FRANCIS    BOWEN, 

ALFORO  PROFESSOR  OF  MORAL  PHILOSOPHY   IN  HARVARD  COLLEGE. 


0^  01 

'UNI 


**Nam  neque  decipitur  ratio,  nee  decipk  unquam." 

Mantlius. 

IP  THE         ^ 

VERSIT' 

BOSTON: 
JOHN     ALLYN,     PUBLISHER, 

1886. 


Entered  according  tc  Act  of  Congress,  in  the  year  1864,  by 
SEVER     AND     FRANCIS, 

in  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


NINTH     EDITION. 


University  Press  :  John  Wilson  &  Son, 
Cambridge. 


r*S*   OP  THE 

:UNIVEESIT7] 
PREFACE 


rpHE  revival  of  the  study  of  Logic,  at  least  in 
JL  England  and  America,  as  an  important  ele- 
ment of  a  University  education,  dates  only  from  the 
publication  of  Dr.  Whately's  treatise  on  the  subject, 
little  over  thirty  years  ago.  Yet  so  much  has  been 
accomplished  for  the  advancement  of  the  science 
during  this  short  period,  that  this  treatise,  with  all 
its  excellences,  must  be  admitted  to  be  now  as  far 
behind  the  times  as  were  the  compilation  by  Al- 
drich,  and  the  meagre  compendium  by  Dr.  Watts, 
the  use  of  which  it  superseded.  Dr.  Whately  lived 
long  enough  to  be  able  to  appropriate  to  himself 
the  epigrammatic  boast,  that  he  had  labored  so  ef- 
fectually as  to  render  his  own  work  useless.  With- 
out the  interest  which  was  awakened  in  the  study 
of  the  science  by  the  publication  of  his  book  and 
the  discussions  which  it  excited,  it  is  not  too  much 
to  say  that  many  of  the  valuable  works  upon  Logic, 
which  have  appeared  during  the  last  thirty  years, 
either  would  not  have  been  written,  or  would  have 
lacked  some  of  their  most  interesting  and  impor- 
tant features.  Sir  William  Hamilton's  own  labors 
in  this  department,  by  which  he  certainly  accom- 
plished more  for  the  science  than  has  been  done  by 
any  one  man  since  Aristotle,  began  with  an  elabo- 


IV  PREFACE. 

rate  article  on  Dr.  Whately's  treatise  in  the  Edin- 
burg  Review,  a  paper  which,  as  he  has  himself 
declared,  contains  the  germs  of  all  his  subsequent 
discoveries.  Besides  what  Hamilton  has  accom- 
plished, the  publications  within  this  period  of  Pro- 
fessor Mansel,  Dr.  Thomson,  Mr.  De  Morgan,  Mr. 
Boole,  Mr.  J.  S.  Mill,  and  a  host  of  others,  have 
given  an  entirely  new  aspect  to  the  science.  Among 
recent  American  works  upon  Logic,  honorable  men- 
tion ought  to  be  made  of  those  by  Mr.  Tappan,  and 
by  Dr.  W.  D.  Wilson  of  Geneva. 

The  only  hope  that  this  volume  may  be  found 
to  be  of  some  use  consists  in  the  fact,  that,  as  I  was 
the  last  to  enter  the  field,  I  have  been  able  to  profit 
by  the  labors  of  my  predecessors.  Certainly  it 
could  not  have  been  written  without  their  aid,  and 
one  of  the  chief  objects  held  in  view  in  the  prepa- 
ration of  it  has  been  to  gather  together,  and  digest 
into  system,  their  several  improvements  and  eluci- 
dations of  the  science.  At  the  same  time,  the 
work  would  not  have  been  carried  on  in  the  same 
spirit  in  which  they  began  it,  if  I  had  not  ventured 
respectfully  to  dissent  from  some  of  their  doctrines, 
and  even  to  present  some  opinions  which  will  very 
likely  be  found  to  have  no  other  merit  than  that 
of  originality.  As  Le  Clerc  remarks,  in  introducing 
his  own  lucid  and  thoughtful  compendium  of  the 
science  to  the  reader's  notice,  "si,  in  haece  Logica, 
nihil  esse  novi,  aut  pleraque  nova  dixerim,  lector  em  perinde 
fefellero" 

When  Dr.  Whately  wrote,  it  was  not  so  frequent 
a  practice  as  it  has  since  become  for  English  schol- 
ars to  profit  by  the  labors  of  their  German  breth- 
ren, and  hence  some  of  the  greatest  deficiencies 
of  his  book.  It  cannot  be  said  that  the  study  of 
Logic  ever  declined  in  the  schools  of  Germany,  as 


PREFACE.  '  V 

it  did  in  those  of  France,  England,  and  this  country. 
Upheld  for  a  time  by  the  genius  of  Leibnitz  and 
the  indefatigable  industry  of  Wolff,  it  was  at  last 
reduced  to  rigorous  system,  its  boundaries  were 
fixed,  and  its  relations  to  Psychology  and  Metaphys- 
ics accurately  determined,  by  the  master  mind  of 
Kant.  Though  this  great  Metaphysician  prepared 
no  distinct  work  upon  the  subject,  the  volume  re- 
lating to  it  which  passes  under  his  name  being  a 
mere  compilation  from  his  loose  notes  by  Jasche, 
the  science  has  profited  more  by  his  labors  than  by 
those  of  any  other  Continental  writer  of  modern 
times.  Indeed,  the  publication  of  his  "  Criticism  of 
Pure  Keason"  formed  hardly  less  an  era  in  the  his- 
tory of  Logic  than  in  that  of  Metaphysics.  In  one 
respect,  it  is  true,  it  had  an  injurious  influence,  as 
it  established  the  practice,  which  has  since  become 
wellnigh  universal  in  Germany,  of  modifying  the 
doctrines  of  this  science  in  order  to  furnish  a  basis 
on  which  might  be  erected  any  peculiar  scheme 
of  speculative  Philosophy.  Since  Kant's  time,  a 
multitude  of  treatises  upon  Logic  have  been  pub- 
lished by  German  writers,  about  half  of  them  hav- 
ing no  other  purpose  than  that  of  preparing  the 
way,  and  furnishing  the  materials,  for  some  extrav- 
agant "speculations  in  Metaphysics.  This  mode  of 
treatment  was  carried  to  an  outrageous  extent  by 
Hegel,  who  labored  to  break  down  altogether  the 
boundary  that  had  been  established  by  Kant,  and 
whose  elaborate  work,  bearing  the  name  of  Logic, 
is  a  mere  perversion  and  caricature  of  that  science, 
as  it  is  metaphysical  from  beginning  to  end.  Even 
Trendelenburg,  who  has  contributed  more  than 
any  other  person  to  the  rapid  decline  of  Hegel- 
ianism  in  Germany,  is  not  free  from  blame  in  this 
respect,  his  very  able  work,  Logische  Untersuchungen} 


VI  TREFACE. 

% 

being  devoted  in  great  part  to  building  up  a  phil 
osophical  system  of  his  own. 

But  the  very  prevalence  of  this  abuse  in  Ger- 
many furnishes  an  additional  motive  for  the  study 
of  the  subject.  A  key  to  German  Metaphysics 
can  be  obtained  only  by  a  thorough  mastery  of 
the  principles  and  the  terminology  of  Logic.  To 
some  persons,  perhaps,  this  consideration  may  not 
have  much  weight,  as  they  will  object,  that  it  is 
of  little  use  to  be  able  to  open  the  door,  if  the 
room  contains  little  more  than  rubbish.  Still  I 
cannot  but  believe  —  and  the  opinion  is  founded 
on  considerable  experience  as  an  instructor  in 
both  departments  —  that  a  fair  knowledge  of  Log- 
ic is  a  natural,  and  even  an  indispensable,  prepara- 
tion for  the  successful  pursuit  of  Psychology  and 
Metaphysics ;  —  may  I  not  add,  of  any  philosoph- 
ical speculations  whatever?  It  appears  certain, 
that  the  University  lectures  of  Kant,  Fichte,  Schel- 
ling,  and  Hegel  could  not  have  been  made  even 
intelligible,  much  less  instructive,  to  hearers  who 
had  not  previously  acquired  at  least  the  elements 
of  Logical  science.  Hence  the  multitude  of  man- 
uals and  text-books  upon  this  subject,  which  have 
appeared  in  Germany  during  the  last  three  quar- 
ters of  a  century,  many  of  them  having  passed 
through  numerous  editions,  and  each  betraying 
very  plainly  the  particular  system  of  Philosophy 
to  which  it  was  intended  to  serve  as  an  introduc- 
tion. Some  familiarity  with  the  principles  of  Log- 
ic appears  essential  for  a  thorough  comprehension 
even  of  the  metaphysical  doctrines  of  Sir  William 
Hamilton,  which,  both  in  their  philosophical  and 
theological  bearings,  seem  likely  to  exert  a  consid- 
erable influence  over  English  and  American  minds 
for  many  years  to  come. 


PREFACE.  Vll 

$ 

Hamilton's  "Lectures  on  Logic"  are  marked 
with  the  irevitable  defects  of  a  posthumous  pub- 
lication, the  larger  portion  of  which  was  probably 
never  intended  by  the  author  to  be  given  to  the 
public ;  and  though  very  ably  edited  by  Professor 
Mansel  and  -Mr.  Veitch,  they  present  a  mass  of 
crude  material  from  which  a  knowledge  of  the 
peculiar  doctrines  of  the  writer  cannot  be  ex- 
tracted but  with  considerable  difficulty.  Indeed, 
the  "  Lectures,"  which  form  the  body  of  the  book, 
were  evidently  prepared  in  great  haste,  when  the 
author's  appointment  to  the  Professorship  in  this 
department,  in  1836,  obliged  him  to  collect  at 
short  notice  the  materials  for  an  extended  course 
of  instruction.  He  appears  to  have  met  this  sud- 
den call  by  hurriedly  translating  a  series  of  ex- 
tracts from  the  most  approved  German  text-books, 
especially  those  of  Kru'g,  Esser,  and  Bachmann, 
merely  interpolating  here  and  there  some  of  the 
comments,  corrections,  and  additions  which  could 
not  fail  to  occur  to  so  rich  a  mind  as  his,  while 
traversing  so  broad  and  familiar  a  field.  These 
Lectures,  containing  only  a  glimpse  of  one  feature 
of  the  peculiar  system  which  has  since  become 
identified  with  his  name,  he  seems  to  have  re- 
peated from  year  to  year,  during  his  whole  period 
of  office,  with  no  material  enlargement  or  altera- 
tion of  the  manuscript,  though  doubtless  inserting, 
from  year  to  year,  many  extemporaneous  exposi 
tions  of  his  corrections  of  the  leading  doctrines 
of  Logical  science,  as  these  occurred  to  him  at  suc- 
cessive periods.  The  whole  transaction  seems  to 
me  to  afford  an  instructive  comment  on  the  futility 
of  what  is  called  the  Professorial  mode  of  teaching, 
which  has  always  prevailed  in  the  University  of 
Edinburgh,  and  which  consists  in  getting  up  very 


Vlll  PREFACE. 

hastily  a  course  of  lectures  during  the  teacher's 
first  year  of  office,  and  repeating  them,  parrotrlike, 
from  year  to  year,  without  any  regular  use  of  a 
text-book  or  manual  of  instruction.  If  such  lec- 
tures contain  anything  really  valuable,  in  addition 
to  what  is  already  before  the  world,  they  are  apt 
very  soon  to  find  their  way  to  the  press ;  if  they 
are  of  little  worth,  they  are  almost  sure  to  be 
repeated,  with  little  alteration,  to  one  class  after 
another,  and  with  as  little  profit  to  the  hearer  as 
exercise  to  the  reader.  It  may  be  doubted  wheth- 
er the  most  fertile  and  best>trained  minds,  at  least 
in  the  speculative  sciences,  are  capable  of  prepar- 
ing every  year  an  entirely  new  course  of  lectures, 
without  either  filling  them  with  crudities  and  tru- 
isms, or  lapsing  into  paradox  and  extravagance, 
such  as  have  too  frequently  characterized  the  pro- 
ductions of  German  Professors. 

With  all  his  amazing  activity  of  mind  and  pro- 
digious erudition,  Hamilton  appears  to  have  been 
either  too  indolent,  or  too  critical  of  his  own  labors, 
to  be  able,  without  great  delays,  to  digest  his  mate- 
rials into  a  shape  fit  for  publication.  He  was  not 
an  adept  in  the  very  low,  but  very  necessary,  art 
of  book-making.  But  for  his  controversy  with  Mr. 
De  Morgan,  I  doubt  whether  he  would  ever  have 
worked  up  into  form  as  much  as  he  did  of  his 
"  New  Analytic  of  Logical  Forms,"  the  publication 
of  which  was  promised  as  far  back  as  1846.  Stim- 
ulated by  opposition,  however,  though  impeded 
by  ill-health  during  the  later  years  of  his  life,  he 
appears  to  have  labored  strenuously,  after  the  last- 
mentioned  date,  to  fulfil  this  promise.  Death  sur- 
prised him  long  before  he  had  completed  his  prep- 
arations; and  out  of  the  mass  of  fragmentary  ma- 
terials which  were  found  among  his  papers,  with 


PREFACE.  IX 

some  aid  from  the  few  critical  and  controversial 
articles  that  he  had  already  printed,  his  editors 
pieced  together,  with  great  difficulty,  the  imperfect 
view  of  his  improved  system  of  Logic,  which  ap- 
pears as  a  long  Appendix  to  the  volume  of  his 
Lectures.  The  manuscripts  which  they  selected 
and  arranged  were  judiciously  printed  just  as  he 
left  them,  and  with  very  little  editorial  comment. 
The  reader  must  gather  from  them  as  best  he 
may,  always  keeping  in  view  the  date  attached 
to  each  fragment,  a  connected  view  of  Sir  William 
Hamilton's  latest  doctrines  upon  the  subject.  This 
posthumous  work  has  at  least  one  odd  character- 
istic, as  the  body  of  the  work  and  the  Appendix 
flatly  contradict  each  other,  by  giving  opposite 
views  of  the  science  to  which  they  relate. 

These  are  the  sources  whence  I  have  endeav- 
ored to  collect  the  materials  for  a  general  survey 
of  the  science  of  Logic  in  its  present  state,  em- 
bracing what  is  common  to  all  systems,  and  a  re- 
view of  most  of  the  questions  relating  to  it  which 
are  still  open  to  discussion.  Among  English  au- 
thors, after  Sir  William  Hamilton,  I  have  been 
chiefly  indebted  to  Professor  Mansel ;  for  without 
the  aid  afforded  by  his  Prolegomena  Zogica,  and  the 
notes  and  supplementary  matter  appended  to  his 
edition  of  Aldrich,  of  which  Hamilton  justly  re- 
marks that  la  sauce  vaut  mieux  que  le  poisson,  this 
book  would  have  cost  me  much  more  labor,  and 
yet  would  have  wanted  what  are  now  its  best 
claims  to  notice.  I  have  also  derived  much  help 
from  the  excellent  "  Outline  of  the  Laws  of 
Thought,"  by  Dr.  Thomson,  the  present  Arch- 
bishop of  York.  Among  the  German  writers,  be- 
sides all  whose  names  have  been  already  men- 
tioned, I  have  made  profitable  use  of  Kiesewetter, 


X  PREFACE. 

Fries,  Beneke,  Dressier,  and  Drobisch,  besides  con 
suiting  a  host  of  others.  Of  the  earlier  logicians, 
it  seems  to  me  that  Burgersdyck,  with  the  anno- 
tations of  Heereboord,  gives  the  clearest  account 
of  the  science  as  it  was  taught  in  the  schools  be- 
fore the  influence  of  Descartes  and  Locke  began 
to  be  felt;  and  that  the  Port  Koyal  "Art  of 
Thinking,"  of  which  an  admirable  translation,  with 
Notes  and  an  Appendix,  by  Mr.  Baynes,  has  re- 
cently been  published,  is  far  the  best  of  the  trea- 
tises on  the  subject  which  were  in  use  during  the 
eighteenth  century.  Throughout  the  work,  I  have 
kept  constantly  in  view  the  wants  of  learners, 
much  of  it  having  been  first  suggested  while  at- 
tempting to  expound  the  science  in  my  own  class- 
room. My  highest  ambition  will  be  satisfied  if  it 
should  be  found  to  be  of  use  to  other  teachers. 

Cambridge,  March,  1864. 


1 


CONTENTS. 


CHAPTER    I. 

*v  PAG» 

Psychological  Introduction 1 

Intuitions  distinguished  from  Concepts  .....  1 

The  Nature  of  Thought 10 

Relations  of  Thought  to  Language 16 

Mental  Characteristics  of  Brutes 18 

The  Formation  of  Concepts          .         .         .         .                  .  19 

Language  aids  Thought    ........  21 

And  is  often  substituted  for  it •  24 


CHAPTER    II. 

Definition  of  Logic 80 

The  Form  distinguished  from  the  Matter  of  Thought      .         •         31 
Universal  distinguished  from  Special  Logic         .         .         .         .34 

Divisions  of  the  Science        .......         36 

Utility  of  the  Study  of  Logic 38 


CHAPTER    III. 

The  Primary  Axioms  of  Pure  Thought 47 

These  Axioms  reduced  to  one  Principle   ^•ni"it*t1iy      .         .  48 

Tins  Principle  explicated  into  three  Axioms        .         •         .  .49 

Analytic  distinguished  from  Synthetic  Thought       ...  52 

The  Principle  of  Synthetic  Thought  explicated  .         •         .  .53 

Hamilton's  Postulate  of  Logic 56 


Xll 


CONTENTS. 


CHAPTER    IV. 


The  Doctrine  op  Concepts     .... 
The  Elements  of  a  Concept         .         .         . 
The  twofold  Quantity  of  Concepts  . 
First  and  Second  Intentions 
The  Relation  of  the  two  Quantities  to  each  other 

Infinitated  Concepts 

The  Quality  of  Concepts  .... 
The  Standards  of  Nominal  and  Real  Definition 
The  Relations  of  Concepts  .... 
The  Laws  of  Homogeneity  and  Heterogeneity 


59 

G2 
G6 
70 

72 
75 

77 
84 
86 
90 


Definition  and  Division *M 


CHAPTER    V. 


The  Doctrine  of  Judgments 


The  Nature  of  the  Copula  .... 
The  Prcdicables  and  the  Categories  . 
The  Quantity  of  Judgments,  Aristotelic  Doctrine 
The  Quality  of  Judgments,  "  " 

Quantity  as  affected  by  Quality,    "  " 

The  Relation  of  Judgments     .... 
Conditional  Judgments        .... 
The  Hamiltonian  Doctrine  of  Judgments  . 

Explication  of  Propositions  into  Judgments . 


105 
109 
112 
120 
123 
125 
127 
128 
132 
141 


CHAPTER  VI. 

The  Doctrine  of  Immediate  Inference 148 

^Squipollence  or  Infinitation        .         .         .         .         .         .  152 

Conversion    ..........  156 

Hamilton's  Doctrine  of  Conversion       .         .         .         .         .  160 

Opposition  and  Integration 162 

Conspectus  of  Judgments  and  Immediate  Inference,  Aristotelic 

Doctrine 166 

Hamilton's  Doctrine  of  Opposition  and  Integration        .        .  168 


CONTENTS.  XUJ 


CHAPTER    VII. 


The  Doctrine  of  Mediate  Inference  :  the  Aristotelic  Anal- 
ysis of  Syllogisms 174 

The  Canon  of  Categorical  Syllogisms 175 

This  Canon  explicated  into  Six  Rules 180 

Dictum  de  omni  et  nxillo         .......  187 

Figure  and  Mood 190 

Reduction  to  the  First  Figure 194 

The  Mood  of  a  Syllogism 197 

The  Technicalities  of  Reduction  exemplified          .         .         .  202 

Conditional  Syllogisms 207 

Disjunctive  Syllogisms 212 

Dilemmas  or  Hypothetico-Disjunctives 215 

Defective  and  Complex  Syllogisms 219 

Sorites 222 

Conspectus  of  the  Aristotelic  Doctrine  of  Syllogisms     .         .  226 

CHAPTER    VIII. 

The  Hamiltonian  Doctrine  of  Syllogisms  ....  228 

Analytic  and  Synthetic  Order  of  Enouncement      .         .         .  228 

Reasoning  in  the  two  Quantities 234 

The  Doctrine  of  the  Figures 239 

The  Unfigured  Syllogism 244 

Hamilton's  System  of  Notation  or  Symbolization  .         .         .  246 

The  Number  of  Moods  increased  by  Quantifying  the  Predicate   .  251 

The  worse  Relation  of  Subject  and  Predicate         .         .         .  253 

Hamiltonian  Table  of  Moods 256 

Falsity  of  the  Special  Rules  demonstrated     ....  259 

Applicability  of  the  different  Figures  to  Deduction  and  Induction  261 

Conditional  Syllogisms  reduced  to  Immediate  Inferences     .         .  264 

CHAPTER    IX. 

Of  Fallacies 267 

Fallacies  in  dictione  improperly  so  called       ....  269 
Division  of  Formal  and  Material  Fallacies         .         .         .         .273 

Syllogisms  of  more  than  Three  Terms ;  Ambiguous  Middle   .  272 


XIV  CONTENTS. 

Undistributed  Middle  ;  Composite  and  Divisive  sense         .         .  278 

Illicit  Process  of  the  Major  and  Minor  Terms        .         .         .  281 

The  Sophism  of  Eubulides,  the  Liar 288 

Sophisms  respecting  the  Quality  of  the  Reasoning         .         .  290 

Violation  of  the  Canons  of  Hypothetical  Reasoning  .         .         .  293 

Material  Fallacies ;  petitio  principii 294 

Fallacy  of  the  Impossibility  of  Motion 296 

Ignoratio  denchi .........  298 

Argumentum  ad  ignorantiam 300 

Non  Causa  pro  Causa;  post  hoc,  er ft  propter  hoc     .         .         .  306 

Jynava  Ratio 309 

Achilles  and  the  Tortoise 312 


CHAPTER    X. 

Aiplied  Logic 314 

Science  formed  by  Analysis  and  Synthesis    .         .         .         .  317 

Classification  in  Science 322 

The  Relation  of  Cause  and  Effect 324 

Necessary  Cognitions  a  priori  .......  328 

These  Cognitions  not  mere  Laws  of  Thought        .         .         .  330 

Elements  of  our  Concepts  of  Individual  Objects        •         .         .  334 

The  preliminary  Classifications  of  Science    ....  340 

Science  advances  through  the  improvement  of  Classifications      .  343 

Failure  of  the  attempts  made  to  classify  the  Sciences     .        .  346 


CHAPTER    XI. 

Demonstrative  Reasoning  and  Deductive  Evidence   .  .    351 
Demonstration  applicable  to  mere  Concepts,  not  to  Real  Things     352 

Why  Mathematical  reasoning  is  demonstrative       .         .         .  353 

Mathematical  evidence  not  a  mere  perception  of  identity     .  .     359 

Distinction  between  Pure  and  Applied  Mathematics        .         .  361 

The  Conclusion  not  deduced  from  the  Major  Premise         .  362 

The  only  New  Truth  is  that  enounced  in  the  Subsumption      .  364 

Particular  facts  not  learned,  but  proved,  by  Reasoning        .  ,367 

Different  classes  of  Major  Premises 371 

Technical  terms  used  in  the  Construction  of  Science  .         .  .    374 


CONTENTS.  xv 


CHAPTER    XII. 

Induction  and  Analogy 376 

Want  of  Universality  in  the  Sumption  fatal  to  strict  Reasoning  376 

Induction  and  Analogy  are  means  for  discovering  Truth     .         .  380 

Difference  between  them  illustrated       .....  381 

Analogy  is  Aristotle's  Reasoning  from  Example        .         .         .  382 

Analogy  leads  only  to  Probable  Conclusions  .         .         .  383 

Induction  presupposes  the  correctness  of  previous  Classifications  385 

Uniformity  of  Nature  the  basis  of  Induction  .         .         .  388 

This  Maxim  not  an  Ultimate  Fact 389 

And  not  first  obtained  by  Induction 391 

But  derived  from  the  Principle  of  Causality       ....  395 

What  is  Physical  Necessity 400 

All  Induction  proceeds  by  simple  enumeration  ....  401 

A  universal  Logic  of  Induction  cannot  be  established     .         .  403 

A  General  Fact,  a  Law  of  Nature,  and  a  Cause  distinguished     .  405 

How  a  Law  of  Nature  is  discovered     .....  409 
Physical  Causes  proved  by  the  Laws  of  Nature  subsumed  under 

them 414 

Induction  discovers,  the  Law  of  Causality  proves  .         •         .  416 


CHAPTER    XIII. 

The  Sources  op  Evidence  and  the  Causes  of  Error.         .  419 

Intuition  the  basis  of  all  Certainty       .         .         •         .         .  419 

Intuition  of  external  objects  as  external 421 

Memory  as  a  Source  of  Evidence 423 

The  art  of  Writing  an  auxiliary  to  Memory      ....  426 

The  experience  of  others  a  necessary  aid       ...         .  427 

Testimony  distinguished  from  Authority 428 

And  Veracity  from  Competency  ......  430 

Hume's  Argument  against  Miracles  examined  ....  432 

The  Criticism  of  Tradition  and  Ancient  Writings          .         .  433 

The  Theory  of  Probabilities 437 

Moral  Causes  of  Error 445 


/ 


CHAPTER 

PSYCHOLOGICAL  INTRODUCTION. 

Intuitions  distinguished  from  Concepts. — Mental  Characteristics  of  Brute* 
—  Relations  of  Thought  to  Language. 

THE  beginning  of  all  knowledge  is  in  single  acts  of  the 
Perceptive  or  Acquisitive  faculty,  each  "of  which  re- 
lates immediately  to  an  individual  object  or  event.  Such 
acts  are  called  Intuitions  or  Presentations ;  the  former  is  the 
more  generally  received  appellation.  Each  Intuition  gives 
us  a  knowledge  of  its  object  so  far  only  as  this  object  is 
perceived  now  and  here,  and  also  as  it  is  one,  or  undivided, 
though  not  necessarily  indivisible.  To  recognize,  or  know 
over  again,  the  object  as  similar  to  another  thing  perceived 
on  a  former  occasion  or  in  a  different  place,  or  to  analyze  it 
into  its  parts  or  attributes,  or  to  refer  it  to  a  class  of  things 
previously  known,  and  thereby  to  give  it  a  common  name, 
requires  the  aid  of  a  different  and  higher  power  of  the 
mind.  In  receiving  Intuitions,  the  mind  exerts  no  conscious 
activity  whatever ;  it  is  passively  receptive  of  any  impres- 
sions that  may  be  made  upon  it,  and  does  not  in  any  way 
consciously  react  upon  or  modify  those  impressions.  It  is 
like  a  mirror  reflecting  the  objects  that  are  held  up  before 
it,  perhaps  giving  distorted  or  unfaithful  images  of  them 
on  account  )f  the  imperfections  of  its  own  surface,  but  hav- 


2  PSYCHOLOGICAL  INTRODUCTION. 

ing  no  power .  to  change  or  in  any  way  affect  them  by  its 
own  will. 

The  impression  made  upon  my  mind  by  the  portrait  of  a 
friend  which  I  am  now  looking  at,  as  it  hangs  before  me,  or 
by  the  sounds  to  which  I  am  listening  as  they  are  struck 
upon  a  violin  ;  the  image  now  present  to  my  memory  of  the 
relative  whom  I  have  recently  lost ;  the  picture  of  a  water- 
fall in  a  wood  which  my  imagination  at  this  instant  forms ; 
the  consciousness  which  I  have  of  the  present  state  of  my 
own  mind ;  —  all  these  are  Intuitions,  as  each  one  of  them 
relates  to  a  single  object,  and  each  is  immediate,  —  that  is, 
it  does  not  come  through  the  intervention  of  any  other  state 
of  mind.  But  what  is  denoted  by  the  word  man,  sound,  or 
waterfall,  is  not  an  Intuition,  for  it  does  not  refer  to  one  ob- 
ject only,  but  to  many.  Man,  for  instance,  includes  under 
it  John,  Thomas,  William,  and  many  others ;  and  it  does 
not  convey  a  complete  image  of  any  one  of  these  persons, 
but  only  a  partial  representation  equally  applicable  to  any 
of  them.  John,  when  considered  simply  as  man,  is  not 
regarded  as  he  really  is,  that  is,  as  possessing  all  his  indi- 
vidual attributes  and  peculiarities,  but  only  as  having  those 
attributes  which  he  possesses  in  common  with  all  other 
men  ;  he  is  not  viewed  immediately,  but  only  through  the 
medium  of  what  is  called  a  Concept,  or  a  Thought  of  what 
is  common  to  many.  These  words,  therefore,  man,  sound, 
waterfall,  and  all  other  common  names,  do  not  denote  In- 
tuitions, but  Thoughts. 

The  Perceptive  or  Acquisitive  faculty,  through  which 
we  receive  Intuitions,  as  it  is  a  merely  passive  power,  or  a 
capacity  of  being  affected  in  a  certain  way,  constitutes  what 
may  be  called  the  receptivity  of  the  mind.  The  Thinking 
or  Elaborative  faculty,  —  i.  e.  the  Understanding,  —  as  it 
has  no  Intuitions  of  its  own,  but  voluntarily  reacts  upon 
and  modifies  those  received  from  the  Perceptive  faculty, 
comparing  them  with  each  other,  and  thereby  combining 


INTUITIONS  DISTINGUISHED   FROM   CONCEPTS.  3 

them  into  one  Thought,  or  disjoining  them  as  dissimilar  or 
incompatible,  belongs  to  the  spontaneity,  or  self-activity,  of 
the  intellect. 

In  the  ordinary  exercise  of  our  faculties,  Intuitions  are 
so  intermingled  with  Thoughts,  so  quickly  pass  into  them, 
and  are  so  closely  connected  with  them,  that  it  is  difficult 
to  illustrate  the  distinction  between  the  two  by  giving  an 
example  of  an  Intuition  so  isolated  and  peculiar  that  there 
will  be  no  danger  of  confounding  it  with  any  portion  of  a 
voluntary  and  more  complex  process  of  mind.  But  a  good 
illustration  may  perhaps  be  found  in  the  case,  so  frequently 
referred  to,  of  a  person  born  entirely  blind,  and  subsequent- 
ly enabled  by  a  surgical  operation,  for  the  first  time,  to  see. 
Suppose  that  the  first  visual  sensation  given  to  such  a  person 
were  that  of  a  flash  of  red  light.  This  sensation,  it  is  evi- 
dent, would  be  to  him  entirely  peculiar  or  sui  generis.  H< 
could  not,  at  first,  refer  it  to  any  class  of  things  with  which 
he  was  formerly  acquainted ;  he  could  not  give  it  a  name  ; 
he  could  not  analyze  it  into  parts  or  attributes.  He  did 
not  will  to  produce  or  to  modify  it ;  it  comes  to  him,  so  to 
speak,  of  its  own  accord.  He  could  know  it,  but  not  recog- 
nize it,  as  the  presentation  of  an  entirely  new  object,  by 
which  his  mind  was  involuntarily  affected  in  a  new  and  sur- 
prising manner.  Such,  we  may  suppose,  are  the  Intuitions 
of  brutes ;  and  the  faculty  of  Intuitions,  as  the  Perceptive 
or  Acquisitive  faculty  may  be  called,  —  a  mere  receptivity, 
unmodified  by  any  voluntary  act  of  the  patient, — is  proba- 
bly the  most  prominent  of  the  few  mental  powers  which 
brutes  possess  in  common  with  man.  In  respect  only  to 
Intuitions  produced  in  him  by  external  causes,  man  has  no 
advantage  over  the  lower  animals. 

But  although  all  our  knowledge  begins  in  Intuitions,  it 
does  not  end  with  them.  In  man,  the  mere  receptivity  of 
mind  is  so  soon  modified  by  its  spontaneity,  —  the  mere  In- 
tuition so  quickly  passes  into  voluntary  or  consciously  active 


4  PSYCHOLOGICAL  INTRODUCTION. 

Thought  properly  so  called,  —  that  we  can  hardly  tell  where 
the  one  ends  and  the  other  begins.  To  recur  to  the  case 
just  mentioned  ;  the  moment  the  person  who  has  now  first 
received  his  sight  begins  to  consider  or  reflect  upon  the  new 
presentation  that  has  thus  been  made  to  him,  he  probably, 
in  a  certain  sense,  recognizes  it  as  a  new  sensation,  —  that  is, 
he  refers  it  to  a  class  of  feelings  with  which  he  was  former- 
ly acquainted,  as  coming  to  him  through  the  other  senses, 
and  which,  as  similar  in  some  respects,  though  different  in 
others,  he  has  ranked  together  and  called  by  one  name, 
"  sensations  "  or  "  feelings."  Such  recognition  is  an  act  of 
Thought  properly  so  called.  It  includes  comparison  of  this 
Intuition  with  others,  and  a  conscious  discrimination  of 
those  respects  in  which  it  is  similar  to  others  from  those  in 
which  it  is  unlike  them.  The  Perceptive  faculty  gives  us 
Intuitions  of  single  objects,  each  of  which  is  to  us  a  distinct 
unit,  having  no  connection  or  relation  with  anything  else ; 
the  Understanding,  a  higher  faculty,  gives  us  Thoughts,  or 
enables  us  to  analyze  each  thing  into  its  parts  or  attributes, 
and  thus  to  recognize  its  various  points  of  resemblance  and 
difference,  and  so  to  form  classes  of  things.  The  former 
power  furnishes  the  rude  material  — "  the  Matter,"  as  it 
is  technically  called  —  of  our  knowledge ;  the  latter  supplies 
"the  Form,"  elaborating  and  disposing  this  rude  material 
in  a  systematic  way,  or  according  to  regular  laws,  by  throw 
ing  it  into  groups,  so  as  to  render  it  conceivable  to  Thought. 
Hence  the  Understanding  has  been  called  the  unifying 
faculty,  by  which  the  many  is  reduced  to  unity. 

If  we  look  out  of  a  window  for  the  first  time  upon  a 
landscape  that  is  entirely  new  to  us,  the  momentary  glance 
gives  us  only  an  Intuition  of  the  scene,  or  a  confused  knowl- 
edge of  it  as*  one  whole,  without  any  distinction  of  parts, 
and  without  recognition  of  any  of  these  parts  as  former 
objects  of  knowledge.  This  is  because  the  Understanding 
requires  time  to  do  its  work.     But  if  we  dwell  long  enough 


INTUITIONS   DISTINGUISHED   FROM   CONCEPTS.  5 

upon  the  scene,  first,  we  recognize  (or  know  over  again) 
one  familiar  set  of  objects,  and  call  them  trees  ;  then,  other 
classes  of  objects  previously  known,  and  call  them  respec- 
tively buildings,  rocks,  hills,  &c.  Lastly,  we  consider  the 
relations  of  these  objects  and  classes  of  objects  to  each 
other  and  to  similar  objects  formerly  known,  in  respect  to 
distance,  magnitude,  color,  &c. ,  and  are  thus  enabled  to 
think  the  landscape  as  a  whole.  This  Thought  contains  a 
far  more  perfect  knowledge  than  the  Intuition,  which  was 
all  that  the  senses  gave  us  at  the  first  momentary  glance. 

Now,  how  much  is  implied  in  the  successive  recognition 
of  the  component  parts  of  this  knowledge  as  objects  previ- 
ously known,  and  therefore  appropriately  designated  by  a 
familiar  name  ?  Of  course,  as  the  landscape  is  supposed  to 
be  now  seen  for  the  first  time,  we  do  not  recognize  any  in- 
dividual tree,  building,  or  hill  in  it  as  precisely  the  same 
object  that  we  have  formerly  seen.  We  mean  only  that 
we  recognize  it  as  similar  to  some  former  objects  of  knowl- 
edge ;  that  is,  having  seen  many  objects  which  agreed  with 
each  other  as  similar  in  many  of  their  parts,  —  as  possessing 
trunks,  branches,  and  leaves,  —  we  have  formed  them  into 
one  class,  and  called  them  trees.  The  object  in  the  new 
landscape  is  then  recognized,  not  as  familiar  in  itself,  but  as 
belonging  to  a  familiar  class  of  things ;  we  do  not  recognize 
it  as  an  Intuition,  but  as  a  Concept,  —  not  as  this  tree,  but 
as  a  tree.  Conception  is  that  act  of  the  Understanding  or 
Thinking  faculty  whereby  we  unite  similar  objects  into  one 
class  by  overlooking  their  points  of  difference  and  forming 
their  common  attributes  into  one  Concept  or  Thought,  the 
name  of  which  thus  becomes  the  common  name  of  all  the 
individuals  included  in  the  class.  Here,  again,  the  unify- 
ing  office  of  the  Understanding  appears ;  the  Concept  re- 
duces the  many  to  unity,  —  brings  together  many  objects 
into  one  Thought  or  many  attributes  into  one  subject. 
Thus  we  are  properly  said  to  know  many  objects  which  we 


6  PSYCHOLOGICAL  INTRODUCTION. 

have  never  seen ;  for,  through  hearing  or  reading  descrip- 
tions of  them,  we  have  formed  a  right  Concept  of  what 
they  are,  and  thus  are  enabled  to  recognize  —  i.  e.  know 
them  over  again — and  call  them  by  their  appropriate  name, 
when  we  do  see  them.  But  this  evidently  is  only  mediate 
knowledge,  and  is  more  or  less  imperfect  and  inadequate, 
depending  on  the  scantiness  or  fulness  of  the  Concept. 
As  Mr.  Mansel  remarks,  a  Concept  "  is  not  the  adequate 
and  actual  representative  of  any  single  object,  but  an  inad- 
equate and  potential  representative  of  many."  And  again, 
"  it  is  not  the  sensible  image  of  one  object,  but  an  intelligi- 
ble relation  between  many." 

Concepts  can  never  come  to  us  from  without,  for  the  ex- 
ternal world  has  no  Concepts.  It  has  not  even  Intuitions 
or  Percepts,  but  only  real  objects,  —  that  is,  persons  and 
things,  and  their  marks  or  attributes.  Every  real  object 
has  an  indefinite  or  countless  number  of  such  attributes  ; 
for,  however  long  and  carefully  we  may  observe  it,  we  can 
never  be  sure  that  we  have  ascertained  all  its  elements  and 
qualities.  Carry  the  chemical  analysis  of  it  one  step  further 
than  before,  or  place  it  in  new  relations  with  other  real  ob- 
jects, and  it  will  manifest  new  properties  or  activities,  the 
existence  of  which  was  formerly  unsuspected.  Observation, 
which  proceeds  by  a  series  of  Intuitions,  can  make  known 
to  us  an  indefinite  number  of  these  attributes,  but  can  never 
exhaust  them.  Hence  the  knowledge  which  we  can  ac- 
quire by  Intuition,  though  constantly  increasing  in  fulness 
and  complexity,  can  never  become  complete,  and  is  always 
attended  with  some  uncertainty;  as  any  conclusions  that 
we  form  respecting  the  object  may  be  vitiated  by  the  pres- 
ence of  a  quality  or  element  of  whose  existence  we  were 
ignorant.  Moreover,  the  limited  compass  and  finite  powers 
of  the  human  mind  cannot  take  in  at  once  all  even  of  those 
attributes  whose  presence  is  perfectly  known.  The  image 
or  representation  of  the  object  in  our  minds  immediately 


INTUITIONS  DISTINGUISHED    FROM   CONCEPTS.  7 

becomes  confused,  when  we  attempt  to  make  it  grasp  too 
much,  or  to  comprehend,  in  truth,  more  than  a  very  few  of 
the  known  attributes.  Giving  up  the  attempt  at  complete- 
ness, then,  we  form  a  Concept  of  the  object  embracing 
comparatively  few  of  its  ascertained  qualities,  but  selecting 
those  which  are  most  distinctive  and  essential,  in  order 
thereby  more  readily  to  discriminate  it  from  other  objects 
of  a  different  class.  Such  a  Concept  is  certainly  incomplete, 
but  it  is  clear  in  proportion  to  the  narrowness  of  its  dimen- 
sions. We  can  more  easily  grasp  it  in  thought,  and  con  • 
template  it  at  once  in  its  entireness,  because  it  has  so  little 
complexity.  On  the  other  hand,  the  lack  of  fulness  is  apt 
to  render  the  boundaries  of  the  Concept  somewhat  less  dis- 
tinct. Consequently,  any  object,  so  far  as  it  is  known  only 
mediately,  or  through  such  a  Concept,  is  known  only  in  a 
few  of  its  leading  attributes ;  and  it  may  even  be  doubtful 
whether  another  object,  which  resembles  it  in  these  attri- 
butes, but  departs  very  widely  from  it  in  others,  ought  to  bo 
ranked  in  the  same  class  with  it,  and  called  by  the  same 
name,  or  not.  If  my  Concept  of  tree,  for  instance,  is  limit- 
ed to  these  few  particulars,  —  a  vegetable  organism  possess- 
ing a  main  trunk,  branches,  and  leaves,  —  it  will  be  doubtful 
whether  many  small  plants  ought  to  be  called  trees  or  shrubs. 
But  if  I  attempt  to  enlarge  the  Concept  by  introducing 
more  attributes,  so  as  to  distinguish  tree  fully  from  all  other 
plants,  the  idea  becomes  cumbrous  and  confused ;  we  can- 
not so  easily  embrace  it  in  a  single  act  of  thought. 

While  the  Percept  or  Intuition  belongs  only  to  the  par- 
ticular attribute  or  object  —  this  one  color,  house,  tree,  or 
stone  —  which  has  impressed  it  upon  the  mind,  the  Con- 
cept refers  to  all  the  things  whose  common  or  similar  at- 
tributes or  traits  it  conceives  (con-capio),  or  grasps  together 
into  one  class  and  one  act  of  mind.  Thus,  for  example, 
the  Concept  red  color  includes  all  similar  red  colors  of  any 
object  whatever ;  the  Concept  tree  refers  to  all  trees,  the 


3  PSYCHOLOGICAL  INTRODUCTION. 

Concept  house  to  all  houses,  &c.  And  naturally  enough  ; 
for  though  the  red  or  the  white  of  this  ohject  is  not  the 
identical  red  or  white  of  that  object,  —  is  at  least  numeri- 
cally different  from  it,  and  seWated  from  it  by  the  acci- 
dents of  place  and  time,  the  one  being  perceived  here 
and  the  other  there,  the  one  being  seen  now  and  the  other 
formerly, — yet  as  the  two  produce  exactly  the  same  im- 
pression upon  the  mind,  or  create  the  same  sensation,  they 
are  regarded  as  virtually  the  same  color  for  all  the  purposes 
of  thought.  Thus,  also,  though  any  one  tree  differs  from 
every  other  tree  in  many  other  respects  besides  the  acci- 
dents of  place  and  time,  yet  it  is  common  to  all  trees  to 
have  a  root,  a  trunk,  branches,  and  twigs.  Now  as  the 
Concept  tree  is  discriminated  from  all  other  Concepts  only 
by  possessing  these  four  Marks  or  attributes,  it  must  neces- 
sarily apply  to  all  trees,  which  are  regarded  as  the  same  for 
all  the  purposes  of  thought.  And  so  it  is  with  all  Concepts. 
Hence  they  are  also  called  Universals,  or  General  Ideas. 

As  Esser  remarks,  "  A  Concept  is  the  representation  of 
an  object  through  its  distinctive  Marks ;  —  that  is,  not 
through  those  Marks  which  distinguish  it  from  other  objects 
in  general,  but  from  those  which  come  the  nearest  to  it. 
The  distinctive  Marks  of  an  object  are  evidently  those 
which  make  it  to  be  this  object,  and  not  some  other  one ; 
i.  e.  they  are  its  peculiar  and  essential  Marks.  The  com- 
mon and  unessential  Marks,  therefore,  do  not  necessarily 
belong  to  the  Concept;  if  they  were  added  to  it,  they 
would  not  only  overburden  and  complicate  the  Concept, 
but  would  lessen  its  applicability  to  other  objects  of  the 
same  kind.  Hence  it  is  self-evident  how  the  Concpt  is 
related  to  the  sensible  Intuition.  Namely,  the  Concept  is 
the  Intuition  stripped  of  its  contingent  or  unessential  (in- 
dividual) attributes  or  Marks ;  and  the  Intuition  is  the 
Concept  clothed  with  the  contingent  or  unessential  (indi- 
vidual)  Marks." 


INTUITIONS  DISTINGUISHED   FROM   CONCEPTS.  9 

A  Concept  may  be  derived  from  one  object  as  well  as 
from  many  similar  ones ;  that  is,  it  may  not  represent  an 
actual,  but  only  a  possible,  class  or  plurality  of  things. 
This  may  be  illustrated  by  the  description  which  a  zoolo- 
gist would  give  of  a  newly  discovered  animal,  that  was  too 
unlike  those  formerly  known  to  be  included  in  the  same 
species  with  any  of  them.  Many  slight  peculiarities  of 
such  an  animal  would  be  passed  over  altogether,  as  unes- 
sential either  to  the  class  to  which  it  belonged,  or  to  any 
other.  And  of  the  more  important  Marks,  which  might 
be  presuned  to  be  specific  and  not  individual  in  character, 
those  only  would  be  selected  for  careful  description  which 
would  serve  to  distinguish  the  new  object  from  those  which, 
through  their  similarity  in  other  respects,  might  be  pre- 
sumed to  belong  to  the  nearest  species,  or  those  most  akin 
to  the  strange  specimen.  The  description  thus  formed, 
containing  possibly  not  more  than  two  or  three  Marks, 
would  be  at  once  a  brief  and  clear  Concept  actually  drawn 
from  an  individual,  but  potentially  applicable  to  a  whole 
class,  should  other  specimens  of  it  be  subsequently  discov- 
ered. In  a  similar  manner,  the  mind  may  think  any  in- 
dividual object  under  a  Concept  consisting  of  a  few  well- 
chosen  Marks,  instead  of  knowing  it  simply  by  an  Intui- 
tion as  a  confused  aggregate  of  many  parts  and"  elements, 
as  brutes  would  do.  We  perceive  only  single  things,  for 
such  only  are  presented  to  us  ;  we  think  only  actual  or  pos- 
sible classes  of  things,  for  Nature  does  not  give  us  classes, 
though  she  furnishes  us  the  resemblances  of  things,  through 
which  we  proceed  to  classify  them.  All  classification  is  an 
act  of  the  mind,  and  is  more  or  less  arbitrary,  depending 
on  our  selection  of  the  attributes  or  relations  in  reference 
to  which  we  classify  them. 

It  is  evident  that  Concepts  must  be  much  clearer  repre- 
sentations of  things  than  the  confused  aggregate  of  Percepts 
or  Intuitions  on  which  they  are  founded.     With  their  light 


10  PSYCHOLOGICAL  INTRODUCTION. 

they  irradiate  and  make  clearly  intelligible  everything  to 
which  they  are  referred,  or  with  which  they  come  together 
into  consciousness ;  and  thus  to  explicate  and  make  clear 
through  Concepts  the  perceived  or  represented  objects  is, 
says  Dressier,  what  it  is,  in  the  strict  logical  acceptation  of 
the  word,  to  think.  In  this  sense,  therefore,  to  think  is  to 
make  clear  through  Concepts  something  already  otherwise 
represented  or  known  to  consciousness. 

Esser  says,  "  To  think  is  to  designate  an  object  through 
a  Mark  or  attribute,  or,  what  is  the  same  thing,  to  deter- 
mine a  subject  through  a  predicate."  According  to  Sir 
William  Hamilton,  "  Thought  is  the  comprehension  of  a 
tiling  under  a  general  notion  (Concept)  or  attribute  " ; 
and  again,  "All  thought  is  a  comparison,  a  recognition  of 
similarity  or  difference,  a  conjunction  or  disjunction ;  —  in 
other  words,  a  synthesis  or  analysis  of  its  objects.  In  Con- 
ception, that  is,  in  the  formation  of  Concepts  (or  general 
notions),  it  compares,  disjoins,  or  conjoins  attributes  ;  in  an 
act  of  Judgment,  it  compares,  disjoins,  or  conjoins  Con- 
cepts ;  in  Reasoning,  it  compares,  disjoins,  or  conjoins  Judg- 
ments. In  each  step  of  this  process,  there  is  one  essential 
element;  to  think,  to  compare,  to  conjoin,  or  disjoin,  it  is 
necessary  to  recognize  one  thing  through  or  under  another ; 
and  therefore,  in  defining  Thought  proper,  we  may  either 
define  it  as  an  act  of  comparison,  or  as  a  recognition  of  one 
notion  as  in  or  under  another."  According  to  other  logi- 
cians, Thought  is  the  reduction  of  complexity  and  plurality 
to  unity,  or  the  bringing  together  of  what  is  confused,  vari- 
ous, and  manifold  or  multitudinous  in  our  Intuitions  into 
the  clear  unity  of  consciousness. 

All  these  definitions  evidently  point  to  one  thing,  or  in- 
dicate what  is  substantially  the  same  process.  Comparison 
is  the  means  through  which  we  unite  what  is  similar,  and 
separate  what  is  unlike  or  opposed ;  for  only  through  com- 
parison do  we  recognize  likeness  or  unlikeness,  agreement 


\ 


INTUITIONS  DISTINGUISHED   FROM   CONCEPTS.  11 

or  opposition.  Now  we  analyze,  divide,  and  distinguish 
only  in  order  subsequently  to  bring  together  and  combine. 
We  discriminate  the  various  elements  or  attributes  of  ob- 
jects through  comparison  of  them  with  each  other,  and  then 
unite  them  with  other  objects  and  attributes  according  to 
their  similarities  as  ascertained  by  a  fresh  act  of  comparison  ; 
and  this  union  of  many  things  in  one  class,  this  reduction 
of  a  plurality  of  Intuitions  under  one  Concept  or  general 
notion,  is  the  means  through  which  the  infinite  variety  and 
multitude  of  natural  objects  are  reduced  to  the  limited  com- 
pass of  the  human  understanding,  and  made  intelligible. 
A  new  individual  object  is  to  us  an  isolated  and  incompre- 
hensible thing,  until  we  have  recognized  its  similarity  with 
something  else,  and  thereby  assigned  it  to  a  class,  or  com- 
prehended it  under  a  Concept,  and  given  it  a  common 
name. 

According  to  some  etymologists,  think  comes  from  the 
same  root  as  thick*  and  originally  signified  thickening,  or 
pressing  together  of  many  into  one;  and  this  exactly  de- 
scribes the  special  function  of  the  understanding.  As  we 
have  already  remarked,  while  a  Percept  or  Intuition  is  a  sin- 
gle representation,  limited  to  this  one  thing  which  excited  it 
or  impressed  it  upon  the  mind,  a  Concept  is  a  collective  (gen- 
eral or  universal)  representation  of  a  whole  class  of  things. 
To  make  a  formal  definition,  we  may  say  that  a  Concept 
is  a  representation  made  up  from  several  particular  Percepts, 
through  the  union  of  their  similar  elements.  It  is  through 
Concepts  that  we  think,  —  that  is,  clearly  understand,  com- 
prehend, or  conceive  something ;  for  these  words  mean  pre- 
cisely the  same  thing,  namely,  to  represent  with  clearer 
consciousness  what  was  already  represented  in  our  minds. 

Besides  the  Percept  and  the  Concept,  the  later  German 
philosophers  distinguish  the  so-called  Idea,  as  the  pattem- 

*  The  n  in  think  is  casual,  and  does  not  appear  in  the  participle  thought 
80  in  German,  dick,  denken,  gedacht. 


12  PSYCHOLOGICAL  INTRODUCTION. 

representation,  ideal  Concept,  or  beau-ideal,  by  which  we 
understand  such  a  representation  as  surpasses  or  goes  be- 
yond the  perceived  and  the  conformed  to  experience.  The 
Idea  is  that  whereby  we  think  an  object  in  its  highest  possi- 
ble perfection,  and  consequently  unlike  anything  which  we 
have  actually  witnessed.  Hence  it  does  not  refer,  like  the 
Intuition,  to  a  single  thing,  nor,  like  the  Concept,  to  a 
whole  class  of  things ;  but  it  wholly  surpasses  in  complete- 
ness or  perfection  the  object  to  which  it  is  referred.  Such 
are  the  Ideas  of  the  artist,  moral  and  religious  Ideas,  &c. 

The  Kantians  use  Representations  to  designate  the  genus 
which  includes,  as  its  several  species,  Percepts,  Concepts, 
and  Ideas.  The  aggregate  of  the  Percepts  which  any  one 
has  had  may  be  said  to  constitute  his  experience. 

Intuitions  afford  the  only  sure  means  of  first  creating, 
and  of  subsequently  rectifying  and  enlarging,  our  Concepts. 
Thus,  I  may  have  some  scanty  knowledge,  obtained  by 
reading  perhaps,  of  a  species  of  plant  or  flower  that  I  have 
never  seen.  The  Concept  thus  formed  may  err  both  by 
excess  and  defect ;  by  excess,  because  it  may  include  some 
parts  or  attributes  which  are  not  peculiar  to  this  species,  but 
are  common  to  it  with  many  others ;  by  defect,  because  it 
may  not  comprise  enough  of  the  attributes  common  to  all 
the  plants  in  this  class,  and  peculiar  to  them  or  not  belong- 
ing to  any  other  plants,  to  enable  me  to  recognize  and  dis- 
tinguish an  individual  of  this  species  when  I  see  it.  It  is 
only  intuitive  knowledge,  or  that  gained  by  direct  observa- 
tion, which  can  enable  me  to  correct  these  errors. 

Intuitions,  then,  are  the  only  test  of  the  reality  of  Con- 
cepts ;  for  they  alone  can  determine  whether  the  Concepts 
properly  correspond  to  the  actual  objects  in  nature  which 
they  are  meant  to  describe.  In  this  sense,  Intuitions  are 
not  only  the  beginning,  but  the  basis  and  the  source,  of  all 
our  knowledge.  All  Concepts,  however,  are  not  meant  to 
represent  actual  objects ;  they  may  be  imaginary  or  fanci- 


INTUITIONS  DISTINGUISHED   FROM   CONCEPTS.  13 

fill.  I  can  conceive  a  centaur  or  a  griffin,  though  no  such 
animal  ever  lived.  Yet  even  in  this  case,  though  the  Con- 
cept, as  a  whole,  is  unreal  or  imaginary,  it  must  be  made  up 
only  of  real  parts  or  attributes,  —  that  is,  of  such  as  have 
been  embraced  in  some  preceding  Intuition.  I  have  never 
seen  a  centaur ;  but  I  have  seen  the  head  of  a  man  and  the 
body  of  a  horse,  and  I  can  unite,  in  Thought,  these  real  parts 
into  an  unreal  whole.  So,  again,  I  can  think  or  conceive 
any  combination,  however  fantastic,  of  colors  that  I  have 
previously  seen ;  but  I  cannot  introduce  into  the  painting, 
even  in  Thought,  any  color  that  I  have  never  seen.  A 
person  born  blind,  and  remaining  so,  cannot  conceive  any 
color  whatever ;  just  as  one  who  has  never  had  the  sense  of 
hearing  can  form  no  Concept  of  sound.  Intuitions,  then, 
are  the  basis,  not  only  of  all  Knowledge,  but  of  all  Thought. 

The  perception  which  gives  us  a  new  Intuition  may  take 
place  either  through  the  external  senses,  or  exclusively 
through  that  internal  source  of  knowledge,  sometimes  called 
an  internal  sense,  but  more  properly  denominated  Con- 
sciousness, by  which  we  are  made  aware  of  the  existence 
of  our  own  sensations,  thoughts,  and  feelings. 

Consciousness,  indeed,  is  the  universal  witness  which 
testifies  to  the  reality,  not  only  of  sensation  and  feeling,  but 
of  the  external  perceptions  which  come  to  us  through  the 
outer  senses.  I  see  a  bright  red  color,  I  hear  a  particular 
sound,  only  so  far  as  I  am  conscious  of  that  act  of  seeing 
or  hearing ;  if  I  were  not  conscious  of  it,  it  would  be  to  me 
as  if  it  were  non-existent.  For  to  know,  and  to  know  that  1 
know,  are  phrases  that  designate  one  indivisible  act  of  mind ; 
and  to  know  that  I  know  is  a  phrase  which  means  the  same 
thing  as  to  be  conscious.  Hence,  though  it  is  an  act  of  sense 
whereby  I  perceive  the  red  color  or  hear  the  sound,  it  is  at 
the  same  time  an  act  of  consciousness ;  as,  otherwise,  I  should 
have  no  knowledge  either  of  the  act  of  perception,  or  of  the 
outward  phenomenon  to  the  existence  of  which  it  testifies. 


14  PSYCHOLOGICAL  INTRODUCTION. 

I  am  conscious  also  of  internal  perceptions,  of  hunger, 
pain,  fear,  joy,  etc.  Still  further,  I  am  conscious  of  myself, 
as  the  one  being  that  perceives,  fears,  or  rejoices.  Every 
act  of  consciousness  is  twofold,  testifying  to  the  existence 
both  of  the  subject,  —  that  is,  of  the  being  or  person  who  is 
conscious,  —  and  of  the  object,  —  that  is,  of  the  feeling,  per- 
ception, or  other  phenomenon  of  which  he  is  conscious. 
The  very  language  which  I  am  compelled  to  use  in  making 
known  the  fact  to  another  person  testifies  to  this  duality  of 
the  act.  Any  phrase  used  for  this  purpose  must  contain  at 
least  two  terms,  one  expressive  of  the  subject,  and  the  other 
of  the  object,  of  consciousness.  Thus,  in  the  proposition 
u  I  feel  hunger,"  the  pronoun  "  I "  denotes  the  person  who 
feels,  and  "  hunger "  the  phenomenon  which  is  felt.  In 
some  languages,  the  whole  may  be  expressed  in  a  single 
word,  as  in  the  Latin  "  esurio  " ;  but  the  expression  here  is 
elliptical,  the  "  ego,"  or  the  subject  of  consciousness,  being 
always  understood.  The  two  elements  can  only  be  known 
together,  simultaneously,  and  in  their  relation  to  each  other. 
One  is  not  known  through  the  other,  or  in  consequence  of 
the  other,  or  after  the  other ;  but  they  are  known  together, 
in  one  act  of  mind.  I  cannot  be  conscious  of  hunger  with- 
out, at  the  same  moment  and  in  the  same  act,  being  con- 
scious of  myself  as  feeling  the  hunger. 

All  the  phenomena,  then,  both  of  the  external  and  inter- 
nal world,  are  presented  to  the  mind  each  in  its  distinctive 
or  peculiar  Intuition.  In  other  words,  any  Intuition  differs 
from  every  other  Intuition,  at  least  in  the  relations  of  time 
and  space.  Thus,  two  successive  Intuitions  by  the  same 
person,  of  the  same  thing,  are  distinguishable  at  least  in  thi3 
respect,  that  the  one  preceded  the  other,  or  took  place  at  an 
earlier  time.  In  like  manner, — to  borrow  an  example  from 
Mr.  Mansel,  —  "I  see  lying  on  the  table  before  me  a  num- 
ber of  shillings  of  the  same  coinage.  Examined  severally, 
the  image  and  superscription  of  each  is  undistinguishable 


INTUITIONS   DISTINGUISHED   FROM   CONCEPTS.  15 

from  that  of  its  fellow ;  but  in  viewing  them  side  by  side, 
Ypace  is  a  necessary  condition  of  my  perception ;  and  the 
difference  of  locality  is  sufficient  to  make  them  distinct, 
though  similar,  individuals."  As  already  remarked,  each 
Tntuition  is  of  a  distinct  thing  as  perceived  now  and  here,  — 
that  is,  in  its  own  peculiar  relations  both  to  time  and  space. 
On  the  other  hand,  a  Concept  is  freed  from  these  relations 
of  space  and  time ;  I  can  think  what  is  denoted  by  the 
word  tree,  without  identifying  it  with  this  or  that  particular 
tree,  standing  on  a  particular  spot,  and  seen  at  a  particular 
time. 

As  already  remarked,  it  is  the  capacity  of  Thought  prop- 
erly so  called  which  constitutes  the  immeasurable  superi- 
ority of  the  human  over  the  brute  mind ;  but  it  is  also  true, 
that  the  necessity  of  Thought  arises  from  the  immeasurable 
inferiority  of  man's  intellect  to  that  of  his  Creator.  •  If  the 
human  mind  were  omniscient  and  of  infinite  compass,  it 
would  behold  all  things  intuitively,  and  would  not  be  con- 
fused and  overburdened  by  the  multitude  of  these  single 
cognitions.  But  it  is  far  otherwise ;  the  mind  is  limited 
and  imperfect,  and  can  grasp  at  once  but  few  objects,  — 
according  to  the  common  opinion,  only  five  or  six.  It  can 
permanently  retain  in  memory,  so  as  to  reproduce  at  will,  it 
can  accurately  represent  in  imagination,  only  a  few  of  its 
primary  Intuitions.  We  must  have  recourse  to  the  artifice 
of  Thought ;  we  must  discard  all  individual  attributes  and 
peculiarities,  in  order,  through  meagre  Concepts,  to  rise  to  a 
larger  and  clearer,  though  consciously  imperfect,  compre- 
hension of  a  multitude  of  things.  As  will  be  shown  here- 
after, it  is  precisely  the  scantiness  of  the  general  notion  in 
respect  to  its  import,  which  renders  it  more  comprehensive 
in  respect  to  the  number  of  things  which  it  embraces ;  in 
other  words,  if  we  would  know  more  objects,  we  must 
know  each  of  them  less  perfectly.  Unable  to  master  the 
vastness  and  complexity  of  Nature  by  taking  in  detail  the 


16  PSYCHOLOGICAL  INTRODUCTION. 

objects  which  she  offers  to  us,  each  in  its  separate  Intuition, 
we  throw  them,  through  discarding  their  differences,  into 
groups  and  classes.  The  mind  can  then  grasp  at  once  six 
or  seven  of  these  groups,  instead  of  being  limited,  as  before, 
to  six  or  seven  individuals.  Then,  by  forming  successively 
groups  of  groups,  or  classes  of  a  higher  order  of  generaliza- 
tion, our  mental  horizon  is  enlarged  till  we  can  take  in,  or 
comprehend  (con-prehendo),  all  the  objects  that  we  have 
ever  known.  But  this  is  like  ascending  a  very  high  moun- 
tain, whence,  though  we  obtain  a  broader  view,  the  outlines 
and  colors  of  objects  below  are  but  faintly  seen,  and  many 
are  wholly  lost  in  the  distance. 

The  nature  of  Language  illustrates  this  process  of  the 
formation  of  Thought.  In  fact,  taken  in  its  strictest  sense, 
Language  is  the  expression  of  Thought  only ;  it  has  to  do, 
not  with  Intuitions,  but  with  Concepts.  Intuitions,  from 
their  very  nature,  can  be  designated  only  by  Proper  Names ; 
and  words  properly  so  called  are  Common  Names.  Every 
word  has  a  meaning,  and  is  therefore  susceptible  of  defi- 
nition, or  at  least  of  explanation.  But  a  Proper  Name, 
strictly  speaking,  has  no  meaning ;  as  Mr.  J.  S.  Mill  re- 
marks, it  is  a  sign  which  denotes  this  one  thing,  but  which 
connotes  nothing.  Like  a  pointing  of  the  finger,  it  desig- 
nates the  individual  who  is  meant ;  but  it  says  nothing  as 
to  the  nature  or  character  of  that  individual.  In  so  far, 
indeed,  as  usage  has  limited  one  class  of  names  to  males, 
and  another  to  females,  in  so  far  the  names  connote  sex ; 
and  precisely  to  this  extent  they  cease  to  be  Proper,  and 
become  Common,  Names.  If,  to  a  person  who  does  not  know 
James,  I  say,  "  James  did  this,"  the  effect  is  precisely  the 
same  as  if  I  had  said,  "  A  man  or  boy  did  it."  If  a  word 
is  to  express  an  Intuition,  it  must  be  accompanied  by  other 
words,  or  at  least  be  marked  by  emphasis  or  a  significant 
gesture,  so  as  to  restrict  its  meaning  to  a  determinate  single 
thing  ;  and  these  limiting  words  can  be  dispensed  with  only 


RELATIONS   OF  THOUGHT   TO  LANGUAGE.  17 

when  the  context,  or  the  custom  of  speech,  supplies  the 
necessary  limitations.  For  example  :  "  this  house  now  be- 
fore us,"  "that  house  on  the  hill,"  "the  house  in  Cam- 
bridge which  I  showed  you  yesterday,"  are  phrases  wherein 
the  general  meaning  of  the  word  house  is  narrowed  down 
to  this  or  that  particular  building,  which  may  be  known 
through  an  Intuition.  In  other  cases,  the  context  or  em- 
phasis suffices  to  limit  the  signification  of  such  phrases  as 
"  his  house,"  "  John's  house,"  "  the  house,"  etc.,  to  the  one 
thing  which  was  intended. 

Dr.  Reid  puzzles  himself  in  attempting  to  explain  how  it 
comes  to  pass,  that,  whilst  all  the  objects  and  events  which 
we  perceive  are  individual  or  singular,  all  the  words  in  a 
language  are  general.  But  the  reasons  are  obvious.  First, 
we  cannot  have  countless  words  for  the  innumerable  single 
objects  which  we  perceive,  as  no  memory  could  retain 
them  :  —  think,  for  a  moment,  of  the  myriads  of  leaves, 
blades  of  grass,  insects,  and  other  classes  of  things,  which 
we  are  constantly  beholding.  Secondly,  these  very  in- 
stances show,  that,  at  least  as  far  as  our  perceptions  are 
concerned,  the  similarity  of  objects  is  often  as  great  as  their 
diversity,  and  even  greater.  Thirdly,  one  main  purpose  of 
language  being  the  communication  of  Thought  to  others, 
what  we  need  to  know  or  to  communicate  is  not  so  often 
a  particular  fact  respecting  this  single  object,  as  it  is  a  gen- 
eral truth  respecting  a  whole  class  of  objects ;  we  do  not  so 
often  need  to  say,  Avoid  or  seek  this  one  thing,  as,  Avoid 
or  seek  all  of  which  this  is  a  specimen.  We  are  more  fre- 
quently concerned,  in  our  mental  operations,  with  classes 
than  with  individuals,  though  the  latter  alone  furnish  em- 
ployment for  our  hands.  Fourthly,  many  things  are  usually 
massed  together  even  to  our  perception,  as  individual  trees 
in  a  forest,  and  therefore  can  never  be  exhaustively  desig- 
nated by  one  expression.  By  the  law  of  parsimony,  there- 
&>re,  language  makes  up  its  millions  of  names   or  designa- 


18  PSYCHOLOGICAL  INTRODUCTION. 

dons  out  of  comparatively  few  words,  just  as  its  thousands 
of  words  are  constructed  out  of  some  twenty  or  thirty  ele- 
mentary sounds  or  letters. 

Language,  then,  deals  only  with  groups  or  classes  of 
things;  and  the  process  of  classification  necessarily  4U&- 
cedes  the  formation  of  language.  This  theory  explains  at 
once  the  most  striking  deficiency  of  the  lower  animals,  — 
their  incapacity  of  using  language.  As  they  have  only 
Intuitions,  the  only  names  which  they  can  apply  or  under- 
stand are  Proper  Names,  —  the  appellations  of  this  or  that 
particular  thing.  These  they  can  understand.  A  dog  can 
easily  be  taught  to  know  the  name  of  his  master,  even 
when  pronounced  by  another  person.  They  can  even  be 
taught  to  know  the  names  of  particular  places  and  build- 
ings, so  that  they  can  understand  and  obey,  when  they  are 
told  to  go  to  the  barn,  the  river,  or  the  house.*  But  it  is 
always  the  particular  barn,  or  other  object,  with  which  they 
have  been  taught  to  associate  this  sound  or  significant  ges- 
ture as  its  Proper  Name.  Carry  the  animal  to  a  distant 
place,  near  which  may  be  a  set  of  corresponding  objects, 
and  then  tell  him  to  go  to  the  barn  or  the  river,  and  he  will 
not  understand  the  order  as  applying  to  the  new  set  of 
objects,  but  will  set  off  immediately  for  the  old  building  or 
place,  with  whose  Proper  Name  alone  he  is  familiar.  As 
Kant  remarks,  a  dog  knows  (JcennC)  his  master,  but  does 
not  recognize  him  through  his  peculiar  Marks  or  Attributes 
(erkennC),  and  thereby  properly  discriminate  him  from 
other  persons. 

These  Intuitions,  which  are  common  to  man  and  the 

*  In  Mr.  Lockhart's  amusing  account  of  Sir  Walter  Scott's  first  favorite 
dog,  "  Camp,"  he  says :  "  As  the  servant  was  laying  the  cloth  for  dinner, 
he  would  address  the  dog  lying  on  his  mat  by  the  fire,  and  say,  •  Camp,  my 
good  fellow,  the  Sheriff's  coming  home  by  the  ford  [or  by  the  hill],'  and  the 
sick  animal  would  immediately  bestir  himself  to  welcome  his  master,  going 
out  at  the  back  door  or  the  front  door,  according  to  the  direction  given,  and  ad- 
vancing as  far  as  he  was  able." 


MENTAL  CHARACTERISTICS  OF  BRUTES.        19 

brute,  and  which  are  mere  impressions  passively  received 
by  the  mind,  may  be  stored  up  in  the  memory,  but  out  of 
consciousness,  as  fruits  of  experience ;  they  may  be  subse- 
quently recalled  to  consciousness,  or  reproduced,  either  by 
casual  association  or  voluntary  reminiscence  ;  and,  when  so 
recalled,  they  may  be  re-presented,  or  pictured  forth  to  the 
mind,  by  an  act  of  that  faculty  which  we  usually  call  Im- 
agination. Brutes,  as  well  as  men,  are  capable  of  all  these 
acts  of  Memory,  Reproduction,  and  Imagination,  when  ex- 
ercised upon  Intuitions  alone;  for  they  are  all  implied  in 
dreaming,  and  a  dog  asleep  upon  a  rug  before  the  fire  often 
shows,  by  his  barking  and  growling,  that  he  has  vivid 
dreams.  Man  can  remember  and  reproduce  Concepts  or 
Thoughts,  as  well  as  Intuitions.  Imagination,  whether  in 
man  or  the  brute,  is  concerned  only  with  Intuitions,  as  it 
pictures  forth  nothing  but  definite  images  of  this  or  that 
particular  object  or  event.  Thoughts  properly  so  called 
are  conceived  or  understood,  but  cannot  be  imagined* 

Agreeably  to  what  has  been  said,  the  mental  process  of 
forming  Concepts  may  be  reduced  to  three  steps,  viz. :  — 

1.  Comparison,  whereby,  among  many  attributes  or  ob- 
jects, we  determine  which  are  similar  and  which  are  differ- 
ent or  unlike. 

2.  Combination  or  Reduction  to  Unity,  whereby,  for  in- 
stance, this,  that,  and  the  other  color  are  recognized  and 
identified  as  what  is  usually  called  "  one  and  the  same  " 
shade  or  hue  of  red  ;  or  several  quadrupeds  are  recognized 
as  all  belonging  to  one  class  called  horse. 

3.  Abstraction,^  whereby  we  separate  and  throw  aside 

*  If  this  simple  distinction  had  been  made,  the  old  dispute  between  the 
Nominalists  and  the  Realists  could  never  have  arisen.  The  former  clearlv 
perceived  that  Concepts  could  not  be  imagined;  the  Realists  knew  very  well 
that,  in  thinking:,  our  thoughts  were  concerned  with  something  more  than 
mere  words.     Both  were  right. 

■j-   This  word,  according  to  its  etymology  (abs-traJw,  to  draw  oft  from),  is 


20  PSYCHOLOGICAL  INTRODUCTION. 

—  i.  e.  put  out  of  Thought  —  the  dissimilar  or  incongru- 
ous attributes  which,  if  retained,  would  prevent  the  other 
elements  from  flowing  together  into  unity. 

Each  of  these  steps  evidently  involves  an  act  of  Judg- 
ment, —  that  is,  of  that  function  of  the  Understanding  or 
Thinking  Faculty  whereby  we  affirm  or  deny  one  Intuition 
or  Concept  of  another.  Hence,  we  may  either  consider 
Judgments  as  the  elements  of  Concepts,  or  Concepts  as 
the  elements  of  Judgments.  Logicians  generally  have 
treated  of  the  functions  of  Conception  or  Simple  Appre- 
hension first,  and  those  of  Judgment  afterwards ;  and,  as 
this  arrangement  is  in  some  respects  more  convenient,  I 
shall  follow  their  example,  though  strict  method  would  per- 
haps require  this  order  to  be  reversed. 

All  men  are  capable  of  comparison,  and  of  discerning 
those  similarities  on  which  the  formation  of  Concepts  de- 
pends. But  it  does  not  so  readily  appear  how  many  differ- 
ent persons  are  naturally  led  to  form  the  same  Concepts, 
according  as  circumstances  render  them  familiar  with  simi- 
lar classes  of  things.  This  is  well  explained  by  Dressier. 
Before  the  elements  which  are  common  to  the  constituent 
Intuitions  can  be  really  united  into  Concepts,  they  must  be 
excited  in  consciousness  simultaneously,  or  in  immediate 
succession ;  if  they  arose  only  separately,  and  at  intervals, 
like  disjoined  fragments,  there  would  be  no  mutual  attrac- 
tion to  draw  them  together.  But  when  thus  brought  be- 
fore the  mind  at  the  same  time,  the  synthesis  of  their 
common  elements  into  one  Concept  is  a  perfectly  natural 
process,  in  which  we  need  no  guidance,  "  as  they  flow  to- 
gether by  a  sort  of  spontaneous  attraction  for  each  other, 

properly  applied  to  the  dissimilar  elements  which  are  put  aside  or  aban- 
doned, though,  until  recently,  logicians  used  it  to  designate  the  process  of 
retaining  and  combining  the  similar  elements.  Sir  W.  Hamilton  would  saj 
that  we  prescind  the  similar  which  is  retained,  and  abstract  the  different  which 
is  thrown  off. 


RELATIONS   OF   THOUGHT   TO   LANGUAGE.  21 

each  of  them  being  the  object  of  a  livelier  and  clearer  con- 
sciousness than  any  of  the  dissimilar  elements.  For  exam- 
ple ;  ifl  see  at  once,  or  in  quick  succession,  six  different 
trees,  I  perceive  their  similar  properties  —  i.  e.  root,  trunk, 
branches,  etc.  —  six  times  over,  being  once  for  each  tree, 
and  thus  have  a  livelier  or  stronger  consciousness  of  them 
than  I  have  of  those  which,  as  dissimilar  or  peculiar  to  one 
tree,  I  perceive  only  once.  Moreover,  for  the  very  reason 
that  these  common  elements  are  similar — that  is,  as  they 
have  fewer  points  of  divergence  or  contrast — they  mor^ 
easily  coalesce  and  melt  into  one  Concept."  As  Hamilton 
remarks,  "the  qualities  which  by  comparison  are  judged 
similar  are  already,  by  this  process,  identified  in  conscious- 
ness ;  for  they  are  only  judged  similar  inasmuch  as  they 
produce  in  us  indiscernible  effects." 

But  this  is  not  all.  "  The  Concept  thus  formed  by  an 
abstraction  of  the  resembling  from  the  non-resembling 
qualities  of  objects  would  again  fall  back  into  the  confu- 
sion and  infinitude  from  which  it  has  been  called  out,  were 
it  not  rendered  permanent  for  consciousness  by  being  fixed 
and  ratified  in  a  verbal  sign."  Hence,  Language  is  neces- 
sary, not  only  that  we  may  communicate  our  Thoughts  to 
others,  but  that  we  may  permanently  retain  and  readily 
use  these  Thoughts  for  our  own  purposes.  Concepts  are 
factitious  units,  and  the  particular  attributes  which  consti- 
tute them  are  somewhat  arbitrarily  selected,  being  more  or 
less  numerous,  and  having  greater  or  less  resemblance, 
according  to  circumstances.  A  Concept,  as  we  have  al- 
ready remarked,  cannot  be  pictured  in  Imagination ;  and 
the  presence  of  one  of  the  real  objects  included  under  it 
does  not  necessarily  suggest  the  particular  attributes  out 
of  which  it  was  formed,  to  the  exclusion  of  others  perhaps 
equally  prominent  to  the  eye.  Hence,  a  Name  must  be 
given  to  it,  which  will  be,  of  course,  a  Common  Name  for 
all  the  individuals  contained  under  it;   or  the  factitious 


22  PSYCHOLOGICAL  INTRODUCTION. 

aggregate  will  be  dissolved  and  lost  to  memory  almost  as 
soon  as  formed.  The  name  preserves  the  unity  of  the 
aggregate  just  as  it  was  originally  constituted,  precisely  as 
a  cord  holds  a  bundle  of  things  together,  and  enables  us  to 
handle  many  objects  as  if  they  were  but  one.  The  Mem- 
ory is  then  burdened  with  the  retention  only  of  one  word, 
which,  when  recalled,  by  the  law  of  association  will  suggest 
its  meaning,  instead  of  being  urged  to  remember  a  consid- 
erable number  of  attributes,  which  can  neither  be  sep- 
arately or  collectively  pictured  in  the  Imagination.  An 
Intuition,  on  the  other  hand,  needs  not  to  be  designated 
by  a  Name,  as  the  presence  of  the  object  immediately  ex- 
cites it  anew  in  its  original  perfection,  and  Imagination  can 
re-present  it  almost  as  adequately  and  vividly  as  the  reality. 
But  the  Concept  can  neither  be  retained  in  mind,  nor,  so  to 
speak,  readily  manipulated  in  Thought,  without  the  aid  of 
a  verbal  sign. 

This  mutual  dependence  of  Thought  and  Language, 
each  bearing  all  the  imperfections  and  perfections  of  the 
other,  has  been  admirably  illustrated  by„Hamilton. 

"  Though,  in  general,  we  must  hold  that  language,  as 
the  product  and  correlative  of  thought,  must  be  viewed  as 
posterior  to  the  act  of  thinking  itself,  —  on  the  other  hand, 
it  must  be  admitted,  that  we  could  never  have  risen  above 
the  very  lowest  degrees  in  the  scale  of  thought  without  the 
aid  of  signs.  A  sign  is  necessary  to  give  stability  to  our 
intellectual  progress,  —  to  establish  each  step  in  our  ad- 
vance as  a  new  starting-point  for  our  advance  to  another 
beyond. 

"  A  country  may  be  overrun  by  an  armed  host,  but  it  is 
only  conquered  by  the  establishment  of  fortresses.  Words 
are  the  fortresses  of  thought.  They  enable  us  to  realize 
our  dominion  over  what  we  have  already  overrun  in 
thought,  —  to  make  every  intellectual  conquest  the  basis 
of  operations  for  others  still  beyond.     Or  another  illustra- 


RELATIONS    OF   THOUGHT   TO   LANGUAGE.  23 

tion  :  You  have  all  heard  of  the  process  of  tunnelling,  of 
tunnelling  through  a  sand-bank.  In  this  operation  it  is  im- 
possible to  succeed  unless  every  foot  —  nay,  almost  every 
inch  —  in  our  progress  be  secured  by  an  arch  of  masonry, 
before  we  attempt  the  excavation  of  another.  Now,  lan- 
guage is  to  the  mind  precisely  what  the  arch  is  to  the  tun- 
nel. The  power  of  thinking  and  the  power  of  excavation 
are  not  dependent  on  the  word  in  the  one  case,  on  the 
mason-work  in  the  other ;  but  without  these  subsidiaries, 
neither  process  could  be  carried  on  beyond  its  rudimentary 
commencement.  Though,  therefore,  we  allow  that  every 
movement  forward  in  language  must  be  determined  by  an 
antecedent  movement  forward  in  thought,  still,  unless 
thought  be  accompanied  at  each  point  of  its  evolution  by 
a  corresponding  evolution  of  language,  its  further  develop- 
ment is  arrested.  Thus  it  is  that  tho  higher  exertions  of 
the  higher  faculty  of  Understanding  —  the  classification  of 
the  objects  presented  and  re-presented  by  the  subsidiary 
powers  in  the  formation  of  a  hierarchy  of  notions ;  the  con- 
nection of  these  notions  into  judgments ;  the  inference  of 
one  judgment  from  another;  and,  in  general,  all  our  con- 
sciousness of  the  relations  of  the  universal  to  the  particular, 
consequently  all  science  strictly  so  denominated,  and  every 
inductive  knowledge  of  the  past  and  future  from  the  laws 
of  nature :  not  only  these,  but  all  ascent  from  the  sphere 
of  sense  to  the  sphere  of  moral  and  religious  intelligence  - — 
are,  as  experience  proves,  if  not  altogether  impossible  with- 
out a  language,  at  least  possible  to  a  very  low  degree. 

"  Admitting  even  that  the  mind  is  capable  of  certain  ele- 
mentary Concepts  without  the  fixation  and  signature  of 
language,  still  these  are  but  sparks  which  would  twinkle 
only  to  expire  ;  and  it  requires  words  to  give  them  promi- 
nence, and,  by  enabling  us  to  collect  and  elaborate  them 
into  new  Concepts,  to  raise,  out  of  what  would  otherwise 
be  only  scattered  and  transitory  scintillations,  a  vivid  and 
enduring  light." 


-4  FSYCHOLOGICAL  INTRODUCTION. 

But  Words  are  not  only  signs  and  preservatives,  chej 
are  also  substitutes,  for  Thoughts ;  and  this  peculiarity  of 
Language  is  an  excellence  or  defect  in  it,  according  as  it  is 
or  is  not  judiciously  used.  As  Bishop  Berkeley  remarks, 
"  It  is  not  necessary,  even  in  the  strictest  reasonings,  that 
significant  names  which  stand  for  ideas  should,  every  time 
they  are  used,  excite  in  the  understanding  the  ideas  they 
are  made  to  stand  for.  In  reading  and  discoursing,  names 
are  for  the  most  part  used  as  letters  are  in  algebra,  in 
which,  though  a  particular  quantity  be  marked  by  each  let« 
ter,  yet,  to  proceed  right,  it  is  not  requisite  that,  in  every 
step,  each  letter  should  suggest  to  your  thoughts  that  par- 
ticular quantity  it  was  appointed  to  stand  for."  Having 
once  satisfied  ourselves,  by  spreading  out  in  thought  all  the 
attributes  which  are  combined  in  any  Concept,  —  or,  to  be 
still  more  careful,  by  having  once  called  up  in  Imagination 
a  picture  of  some  one  individual  possessing  all  these  attri- 
butes, and  therefore  contained  in  the  class,  —  that  the 
meaning  of  the  word,  which  is  the  Sign  of  that  Concept 
and  the  Common  Name  of  that  class,  is  within  our  power, 
we  proceed  to  use  that  word  symbolically,  —  that  is,  as  a 
mere  sign,  and  therefore  with  much  more  ease  and  rapidity 
than  if  it  were  necessary  to  stop,  each  time  it  recurs,  and 
repeat  the  process  of  verifying  its  meaning.  Hence  it  may 
be  said  that  the  use  of  language  gives  us  the  power  of 
thinking  in  short-hand ;  words  are  stenographic  thoughts. 
Moreover,  this  abbreviated  expression  of  thought  is  a  great 
help  to  the  memory.*  Having  once  ascertained  by  reflec- 
tion the  relation  of  various  Concepts  to  each  other,  —  that 
is,  having  formed  judgments  and  reasonings,  and  expressed 
them  in  propositions,  —  it  is  a  far  easier  and  shorter  method 
to  remember  the  few  words  which  constitute  such  a  propo- 
sition, than  to  recall  successively  each  of  the  mental  pro- 
cesses which  are  now  embodied  in  it,  and  through  which  it 
was  first  obtained.     Language  is  the  great  repository  of 


RELATIONS   OF   THOUvwIT   TO   LANGUAGE.  25 

thought,  not  only  in  books,  but  in  our  own  minds.  The 
algebraist  easily  recalls  to  mind  a  few  brief  formulas,  which 
enable  him  to  perform  almost  mechanically  long  numerical 
computations,  which  the  mere  arithmetician  must  slowly 
and  painfully  think  out  step  by  step.  Even  when  the 
meaning  of  the  words  is  not  sufficiently  familiar  to  enable 
us  to  perform  the  whole  process  symbolically,  or  by  the  use 
of  words  alone,  we  can  often  do  so  in  part ;  —  that  is,  we 
need  only  to  explicate,  or  spread  out  in  our  minds,  that 
particular  portion  of  their  meaning  which  happens  to  be  all 
that  is  necessary  for  the  special  purpose  which  we  now  have 
in  view.  Thus  I  may  not  know  the  full  meaning  of  a  tech- 
nical term  in  some  science,  or  of  a  certain  verb  in  the  Greek 
language,  and  still  be  enabled  to  use  it  without  error  in  that 
one  of  its  numerous  applications  with  which  use  may  have 
made  me  familiar.  This  symbolic  knowledge,  as  it  was 
termed  by  Leibnitz,  bears  about  the  same  relation  to  the 
full  thought,  of  which  it  is  the  abbreviated  expression,  that 
our  ordinary  cursive  handwriting  does  to  an  ideographic 
system,  or  to  the  picture-writing  of  the  Mexicans. 

On  the  other  hand,  it  should  be  remembered  that  there 
is  peculiar  danger  in  this  use  of  words  as  a  temporary  sub- 
stitute for  thought.  Dr.  Campbell  mentions  it  as  the  rea- 
son why  many  persons,  even  among  the  judicious  and  the 
well-informed,  are  sometimes  led  both  to  talk  and  write 
nonsense  without  knowing  it.  When  the  use  of  words  is 
not  checked  by  a  frequent  recurrence  in  thought  to  the 
precise  limitations  of  their  meaning,  even  the  best  of  us 
are  occasionally  betrayed  into  applications  of  them  which 
a  moment's  reflection  would  prove  to  be  incongruous  and 
absurd.  The  ordinary  safeguard  against  such  blunders  is, 
that,  having  become  familiar  by  use  with  certain  words  in 
their  ordinary  relations  and  connections  with  other  words, 
anything  new  or  peculiar  in  the  combinations  in  which  they 
are  sometimes  found,  or  in  which  we  may  ourselves  be 

2 


26  PSYCHOLOGICAL  INTRODUCTION. 

tempted  to  place  them,  at  once  attracts  our  notice,  and 
puts  us  upon  the  lookout  to  detect  a  possible  absurdity. 
Take,  for  instance,  the  following  stanza,  which  occurs  in 
the  "  Song  by  a  Person  of  Quality,"  written  by  Pope  to 
ridicule  this  very  class  of  blunders,  as  frequently  committed 
by  people  of  fashion  in  their  attempts  to  string  together  in 
verse  the  mere  commonplaces  of  poetical  expression  :  — 

"  Gloomy  Pluto,  king  of  terrors, 
Armed  in  adamantine  chains, 
Lead  me  to  the  crystal  mirrors 
Watering  soft  Elysian  plains." 

As  chains  usually  bind  and  mirrors  reflect,  not  even  the 
smoothness  of  the  measure  can  here  cause  us  to  slide  over 
the  absurdity  of  supposing  Pluto  to  be  armed  by  the  for- 
mer, or  plains  watered  by  the  latter. 

To  avoid  such  blunders,,  it  is  not  enough  to  be  able 
merely  to  explicate  in  thought  the  meaning  of  each  word 
taken  by  itself,  or  separately,  but  the  combination  of  words 
must  express  a  possible  union  in  thought  of  what  is  ex 
pressed  by  them.  Whether  this  can  be  done  can  be  ascer 
tained  only  through  the  process  of  what  Mr.  Mansel  calls 
"  individualizing  our  Concepts,"  —  that  is,  of  calling  up  in 
imagination  a  picture  of  some  particular  thing  denoted  by 
the  words  taken  together,  because  possessing  together  all  the 
attributes  contained  in  such  a  union  of  Concepts.  It  is  only 
by  the  failure  of  the  attempt  to  form  such  a  mental  image, 
that  we  are  led  to  perceive  the  absurdity  of  such  expres- 
sions as  a  bilinear  figure,  an  iron-gold  mountain,  or  a  water- 
ing mirror.  Hence  it  appears,  that  what  is  perfectly  intelli- 
gible in  language,  when  the  words  are  taken  separately, 
may  be  absolutely  inconceivable  in  thought.  I  know  what 
each  of  the  words  bilinear  figure  means  ;  but  such  a  figure 
is  inconceivable,  and  therefore  the  union  of  the  two  words 
is  absurd. 

It  ^vas  remarked  by  Burke,  in  lus  Essay  on  the  Sublime 


RELATIONS   OF  THOUGHT   TO  LANGUAGE.  %      27' 

and  Beautiful,  that  words  are  not  only  used  as  substitutes 
for  thoughts,  but,  through  the  laws  of  association,  they  also 
serve  to  call  up  the  same  emotions  which  are  naturally  pro- 
duced by  the  presence  or  imagination  of  the  real  objects 
which  they  denote.  Thus,  there  are  many  words  which 
have  feelings  of  awe,  sorrow,  or  affright  so  firmly  associ- 
ated with  them,  by  long  habit,  that  the  mere  utterance  of 
them  in  a  sermon  is  enough  to  solemnize  the  minds  of  the 
congregation,  even  before  the  hearers  have  time  to  think  of 
what  they  mean. 

The  doctrine  of  the  Nominalists,  then,  is  true  to  this 
extent,  —  that  very  often,  in  the  use  of  language,  there  is 
nothing  before  the  minds  either  of  the  speakers  or  the 
hearers  but  mere  words ;  and  yet  these  words  are  signifi- 
cantly and  correctly  used,  and  they  answer  their  purpose 
of  exciting  emotion  and  imparting  knowledge.  But  it  is 
also  often  true,  that,  in  the  use  of  words,  all  the  powers 
of  the  Understanding,  or  Thinking  Faculty,  are  in  active 
exercise  ;  —  that  we  compare,  combine,  discriminate,  judge, 
and  discern  new  relations  before  unthought  of,  the  subsidi- 
ary powers  of  the  Memory  and  Imagination,  all  the  while, 
furnishing  their  aid  whenever  needed  ;  and  it  is  only  by 
such  concomitant  activity  of  the  Thinking  power,  that  we 
can  have  full  assurance  that  the  words  in  question  are  cor- 
rectly used,  and  the  boundaries  of  our  knowledge  are  en- 
larged. Thus,  in  the  thoughtful  use  of  words,  we  are 
continually  spreading  out  in  our  minds  the  attributes  of 
which  the  Concepts  are  made  up,  individualizing  them, 
comparing  them  with  each  other,  discovering  new  relations 
between  them,  and  carrying  them  up  into  higher  orders  of 
generalization,  or  extending  them  to  more  objects. 

A  few  remarks  may  be  necessary  in  explanation  of  the 
nomenclature  which  has  been  here  employed.  The  Eng- 
lish words  thinking,  thought,  are  commonly  used,  in  a  very 
vague  and  comprehensive  sense,  to  denote  any  cognitive 


28  PSYCHOLOGICAL  INTRODUCTION. 

act  or  object  of  the  mind.  But,  as  applied  in  Logic,  they 
are  strictly  limited  to  one  well-defined  class  of  our  cogni- 
tive functions.  After  the  illustrations  that  have  now  been 
given,  the  peculiar  characteristics  of  Thought  properly  so 
called  are  perhaps  sufficiently  understood. 

Hamilton  justly  observes,  that  most  of  the  words  which 
signify  operations  of  the  mind  have  a  triple  ambiguity,  for 
they  may  denote  either,  1.  the  faculty ;  or,  2.  the  act ;  or, 
3.  the  product  of  the  act.  To  avoid  this  uncertainty,  the 
Understanding  is  here  used  exclusively  to  denote  the  Fac- 
ulty of  Thinking  in  the  narrower  sense,  or  what  Hamilton 
calls  the  "  Elaborative  Faculty,"  because  it  elaborates,  or 
works  up  into  Thought,  the  raw  material  which  is  furnished 
to  it  by  the  Perceptive  powers.  Like  any  other  faculty, 
the  Understanding  at  any  particular  time  may,  or  may  not, 
be  in  exercise.  Its  function  or  peculiar  office  is  to  think  ; 
hence,  thinking  denotes  the  act,  while  Thought  signifies  the 
product,  of  this  faculty.  As  will  be  shown  hereafter, 
Thought  is  the  generic  term,  for  there  are  three  species 
of  it;  viz.  Concepts,  Judgments,  and  Reasonings  or  Infer- 
ences. The  old  logicians  referred  the  origin  of  these  three 
species  of  Thought  to  as  many  distinct  faculties,  which  they 
denominated  respectively  Simple  Apprehension,  Judgment, 
and  the  Discursive  Faculty.  Of  these,  Simple  Apprehen- 
sion corresponds  very  nearly  to  that  sort  of  Thinking  which 
we  now  call  Conception,  its  products  being  denominated 
Concepts.  In  like  manner,  the  products  of  the  Percep- 
tive or  Acquisitive  Faculty,  hitherto  called  Intuitions,  might 
more  conveniently  be  termed  Percepts,  as  we  should  then 
have  an  English  verb,  perceive,  to  express  the  act  of  that 
Faculty  of  which  these  are  products.  If  it  were  allowable 
to  coin  an  English  verb  to  express  the  act  of  intuition,  an- 
swering to  the  German  anschauen,  analogy  would  direct  us 
to  say  intuit.  The  Discursive  Faculty  (from  discurrere,  to 
run  to  and  fro)  was  so  called  because,  in  Reasoning  or 


INTUITIONS   DISTINGUISHED   FROM   CONCEPTS. 


29 


drawing  Inferences,  the  mind  runs  over  from  one  Judg- 
ment, as  the  Ground  or  Reason,  to  another,  as  the  Conse- 
quence or  Conclusion.  But  the  whole  Understanding  is 
more  properly  called  by  this  name  ;  for,  in  forming  Con- 
cepts, the  mind  runs  over  the  Percepts  or  Intuitions  from 
which  they  are  derived,  in  order  to  separate  the  similai 
elements  from  the  unlike,  and  consciously  to  unite  the  for- 
mer into  one  product  of  Thought. 


30  •     DEFINITION   OF   LOGIC. 


CHAPTER    II. 

DEFINITION   OF  LOGIC. 
Divisions  of  the  Science.  —  Utility  of  the  Study. 

LOGIC  is  the  Science  of  the  Necessary  Laws  of  Pure 
Thought. 

The  Greek  word,  \6yos,  from  which  Logic  is  derived, 
signifies  both  the  inward  thought,  and  the  word  or  outward 
form  in  which  this  thought  is  expressed ;  and  thus  includes 
both  the  ratio  and  the  oratio  of  the  Latins.  This  fact,  and 
the  intimate  connection  which,  as  we  have  already  seen, 
exists  between  Thought  and  Language,  has  caused  some 
writers,  especially  those  who  adopt  the  Nominalist  theory 
to  its  full  extent,  to  maintain  that  u  Logic  is  entirely  con- 
versant about  Language."  ■  But  it  is  not  so ;  for  Logic  is 
primarily  and  essentially  conversant  with  Thought,  and 
only  secondarily  and  accidentally  with  Language ;  that  is, 
it  treats  of  Language  so  far  only  as  this  is  the  vehicle 
of  Thought.  Just  the  reverse  is  true  of  the  science  of 
Grammar,  which  treats  primarily  of  Language,  and  only 
secondarily  of  Thought.  Logic  might  be  called  the 
Grammar  of  Thought. 

Others  have  held  that  "  the  process  or  operation  of  rea- 
soning is  alone  the  appropriate  province  of  Logic."  Bui 
this  is  putting  the  part  for  the  whole,  and  is  as  inadequate 
as  it  would  be  to  restrict  Geometry  to  the  measurement  of 
spherical  bodies,  to  the  exclusion  of  lines,  angles,  plane  sur- 
faces, and  rectilinear  solids.  There  are  three  classes  of  the 
products  of  Thought,  namely,  Concepts,  Judgments,  and 


DEFINITION   OF   LOGIC.  31 

Inferences  or  Reasonings,  with  each  of  which  Logic  is  im- 
mediately concerned,  as,  indeed,  no  one  of  them  can  be 
adequately  discussed  without  consideration  of  both  the  oth- 
ers. If,  on  the  one  hand,  it  can  be  said  that  conception 
and  judgment  are  both  subsidiary  to  the  process  of  reason- 
ing, so,  on  the  other,  judgment  is  the  primary  and  essential 
operation,  of  which  conception  and  inference  are  only  spe 
cial  forms  or  complex  results. 

Pure,  or,  as  it  is  sometimes  termed,  Formal  Thought,  is 
the  mere  process  of  thinking,  irrespective  of  what  we  are 
thinkinc  about.  It  has  already  been  said  that  the  Acquisi- 
tive or  Perceptive  Faculty  furnishes  "  the  Matter,"  while 
the  Understanding  supplies  "the  Form,"  of  our  knowledge. 
This  distinction  between  Matter  and  Form  is  one  of  con- 
siderable importance  in  the  history  of  philosophy.  The 
former  is  the  crude  material  or  the  stuff  of  which  anything 
consists,  or  out  of  which  it  is  made ;  while  the  latter  is  the 
peculiar  shape  or  modification  given  to  it  by  the  artist, 
whereby  it  has  become  this  particular  thing  which  it  is,  and 
not  something  else  which  might  have  been  fashioned  out  of 
the  same  substance.  Thus,  wood  is  the  Matter  of  the  desk 
on  which  I  am  writing,  whilst  the  Form  is  that  which  enti- 
tles it  to  be  called  a  desk,  rather  than  a  table  or  a  chair. 
Vocal  sound  is  the  Matter  of  speech,  and  articulation  is  its 
Form.  It  is  evident  that  these  are  two  correlative  notions, 
each  of  which  implies  the  other :  Matter  cannot  exist  ex- 
cept under  some  Form,  and  there  cannot  be  any  Form 
except  of  some  given  Matter.  But  though  the  two  cannot 
actually  be  separated,  the  mind  can  consider  each  separately 
through  that  process,  called  abstraction,  whereby  the  atten- 
tion is  wholly  given  to  the  one  to  the  exclusion  of  the  other. 
We  may  think  separately  of  the  attributes  which  are  com- 
mon to  a  whole  class  of  Forms,  disregarding  altogether,  for 
the  moment,  the  Matter  of  which  each  of  them  really  con- 
sists.    Borrowing  algebraic  symbols,  the    Matter  in  each 


32  DEFINITION   OF  LOGIC. 

case  may  be  designated  by  a  letter  of  the  alphabet,  the  pe- 
culiar significance  of  which  is,  that  it  stands  for  any  Matter 
whatever,  and  not  for  any  one  in  particular.  Thus,  A  is  B, 
is  the  Form  of  an  affirmative  judgment,  wherein  A  and  B 
stand  for  any  two  Concepts  whatever.  Hence,  whatever  is 
true  of  the  general  formula,  A  is  B,  will  be  true  also  of 
any  such  particular  instances,  as  Iron  is  malleable,  Trees  are 
plants,  &c,  wherein  the  Form  is  associated  with  some  par- 
ticular Matter.  In  saying,  then,  that  Logic  is  concerned 
only  with  the  Forms  of  Thought,  or  Pure  Thought,  or 
Thought  in  the  abstract,  —  for  all  these  expressions  signify 
the  same  thing,  —  we  mean  only,  that  what  is  Material  in 
Thought  is  extralogical,  and,  as  logicians,  we  have  nothing 
to  do  with  it ;  just  as  the  geometer  has  nothing  to  do  with 
the  particular  diagram  on  the  paper  before  him,  except  so 
far  as  it  is  a  symbol,  or  universal  Form,  of  all  possible  fig- 
ures of  the  same  general  character.  As  Hamilton  remarks  : 
"  The  objects  (the  Matter)  of  thought  are  infinite ;  no  one 
science  can  embrace  them  all,  and  therefore  to  suppose 
Logic  conversant  about  the  Matter  of  thought  in  general,  is 
to  say  that  Logic  is  another  name  for  the  encyclopaedia  — 
the  omne  scibile  —  of  human  knowledge.  The  absurdity  of 
this  supposition  is  apparent.  But  if  it  be  impossible  for 
Logic  to  treat  of  all  the  objects  of  thought,  it  cannot  be 
supposed  that  it  treats  of  any ;  for  no  reason  can  be  given 
why  it  should  limit  its  consideration  to  some,  to  the  exclu- 
sion of  others.  As  Logic  cannot,  therefore,  possibly  include 
all  objects,  and  as  it  cannot  possibly  be  shown  why  it  should 
include  only  some,  it  follows  that  it  must  exclude  from  its 
domain  the  consideration  of  the  Matter  of  thought  alto- 
gether; and  as,  apart  from  the  Matter  of  thought,  there 
only  remains  the  Form,  it  follows  that  Logic,  as  a  special 
science  of  thought,  must  be  viewed  as  conversant  exclu- 
sively about  the  Form  of  thought." 

Again,  the  definition  of  Logic  assumes  that  the  process 


DIVISIONS   CF   THE   SCIENCE.  33 

of  Thinking,  like  every  other  operation  in  nature,  does  not 
take  place  at  random,  but  according  to  certain  fixed  Laws 
or  invariable  modes  of  procedure.  There  could  be  no  com- 
munication of  Thought  from  one  mind  to  another,  if  the 
process  of  Thinking  in  all  minds  were  not  subject  to  the 
same  general  rules.  We  follow  these  laws  for  the  most 
part  unconsciously,  as  a  distinct  recognition  of  them  is  not 
by  any  means  necessary  for  correct  thinking ;  just  so,  many 
persons  speak  and  write  correctly  without  any  knowledge 
of  the  grammarian's  rules.  But  they  can  be  discovered 
through  analysis  of  their  results,  and  the  business  of  the 
logician  is  to  search  them  out  and  arrange  them  in  order, 
just  as  the  grammarian's  duty  is  to  set  forth  those  second- 
ary laws  of  Thought  which  control  the  formation  and  the 
use  of  Language.  Logic,  says  Dr.  Thomson,  "  like  philoso- 
phy, of  which  it  is  a  part,  arises  from  a  reflection  of  the 
mind  upon  its  own  processes ;  a  logician  is  not  one  who 
thinks,  but  one  who  can  declare  how  he  thinks." 

But  here  a  distinction  is  to  be  made,  for  Logic  takes  cog- 
nizance not  of  the  contingent,  but  only  of  the  necessary 
and  universal,  laws  of  Thought.  Psychology,  as  the  science 
of  the  mental  phenomena  in  general,  includes,  of  course,  the 
procedures  of  Pure  Thought ;  but  it  includes  them  only  in 
their  contingent  and  phenomenal  character,  as  actually 
existing  now  and  then,  but  not  as  necessarily  existing  at  all 
times.  Logic  does  not  consider  the  subsidiary  processes, 
such  as  Perception,  Memory,  and  Imagination,  through 
which  we  collect  the  materials  for  thinking.  The  operations 
of  the  Thinking  Faculty  are  also  contingently  modified  by 
the  coexistence  of  other  powers  and  affections  of  the  mind ; 
they  are  obstructed  by  indolence,  and  warped  by  prejudice 
and  passion.  Logic  does  not  regard  these  accidental  per- 
versions of  the  Understanding,  but  takes  into  view  only 
those  fundamental  and  absolute  principles,  to  which  all 
Thought  is  necessarily  subject,  and  which  shine  by  their 

2*  C 


34  DEFINITION   OF  LOGIC. 

own  light,  as  they  cannot  he  transgressed  except  by  the 
idiot  or  the  madman.  A  violation  of  one  of  these  Laws  is 
not  so  much  an  error  in  Thinking,  as  a  negation  of  Thought. 
They  are  axiomatic  in  character ;  that  is,  they  cannot  he 
proved  or  deduced  from  higher  principles,  for  such  proof  or 
deduction  would  he  itself  an  act  of  Thought,  and  therefore 
would  presuppose  the  validity  of  the  very  principles  which  it 
was  intended  to  guarantee.  These  Laws  cannot  be  proved, 
hut  they  can  be  enunciated  and  explained ;  when  under- 
stood, their  truth  is  self-evident,  for  they  rest  upon  the 
immediate  testimony  of  consciousness.  As  necessary  and 
universally  known,  they  are  never  consciously  broken ;  but 
we  may  be  betrayed  into  an  apparent  transgression  of  one 
or  more  of  them,  through  an  incautious  yoking  together  of 
certain  words  or  formulas  of  expression,  without  sufficiently 
thinking  of  what  they  denote.  Some  Hibernicisms,  as  they 
are  termed,  are  of  this  character.  The  judge,  who,  when 
puzzled  by  the  ingenuity  of  two  lawyers  who  were  plead- 
ing a  cause  before  him,  exclaimed  in  a  pet,  "  I  believe 
you  are  both  right,"  really  violated  that  universal  Law  of 
Pure  Thought,  called  the  Principle  of  Excluded  Middle, 
which  declares  that,  of  two  contradictory  propositions,  one 
must  be  true,  and  the  other  false.  Logic,  as  it  proceeds 
from  axiomatic  principles,  and  derives  none  of  its  materials 
from  experience,  but  considers  only  those  laws  which  under- 
lie all  experience  and  first  render  it  possible,  is  a  purely  de- 
monstrative science,  like  algebra  or  geometry.  It  treats  of 
those  arguments  only  which  are  certain  and  irrefutable ;  or 
if  it  indirectly  considers  some  of  those  forms  which  come 
short  of  perfect  demonstration,  such  as  Analogy,  Imperfect 
Induction,  and  Example,  it  is  only  for  the  purpose  of  test- 
ing them  by  a  reference  to  the  standard  forms  the  validity 
of  which  they  presuppose,  and  which  they  endeavor,  as  it 
were,  to  approximate. 

Universal  Logic  considers  the  Laws  of  Thought  in  their 


DIVISIONS   OF  THE  SCIENCE.  35 

application,  not  to  this  or  that  special  class  of  objects,  but 
to  all  objects  whatsoever.  This  is  the  Logica  dooms  of  the 
Schoolmen,  and  contains  the  abstract  theory  of  the  science 
in  its  widest  sense,  without  any  of  the  limitations  that  arise 
from  any  special  purpose  or  study  which  the  thinker  may 
have  in  view.  It  corresponds  to  the  science  of  Universal 
Grammar,  which  treats  only  of  those  principles  which  be- 
long to  language  as  such,  and  therefore  are  exemplified  in 
all  languages,  putting  aside  altogether  the  peculiarities  of 
Hebrew,  Greek,  German,  or  any  other  particular  tongue. 
On  the  other  hand,  Special  Logic,  or  the  Logica  utens  of 
the  Schools,  is  the  Logic  of  Mathematics,  or  the  Logic  of 
History,  or  of  any  other  particular  science ;  consequently, 
it  involves  a  consideration  of  the  Laws  of  Thought  so  far 
only  as  they  are  exemplified  or  involved  in  the  processes 
of  this  one  science.  Herein  Logic  becomes  subsidiary  to 
the  objects  of  the  special  inquiry  which  it  is  intended  to 
promote  or  regulate.  It  presupposes  a  knowledge  of  those 
objects,  and  it  forms  an  introduction  to  that  inquiry. 
Hence,  it  is  no  longer  Logic  considered  for  its  own  sake, 
but  it  is  Geometry,  History,  or  some  other  science,  consid- 
ered in  a  logical  point  of  view.  The  discussion  of  it  is 
therefore  relegated  to  treatises  on  that  science  of  which  it 
forms  a  part,  and  for  which  it  is  a  special  preparatory  study. 
Legal  Logic  is  a  part  of  the  science  of  Law.  Mathemati- 
cal Logic  is  an  introduction  or  an  appendage  to  pure  Math- 
ematics. But,  in  what  now  lies  before  us,  it  is  evident  that 
we  have  to  do  only  with  Universal  Logic,  which  is  one, 
while  Special  Logic  is  multiform ;  which  is  independent, 
while  that  requires  an  acquaintance  with  other  objects  of 
study  and  other  modes  of  investigation  ;  which  is  a  part  of 
the  Philosophy  of  Mind,  or  of  Philosophy  itself  in  its  wider 
sense,  while  that  is  a  portion  of  a  comparatively  narrow 
science. 

There  are  certain  other  portions  of  what  has  usual!) 


36  DEFINITION   OF  LOGIC. 

been  called  Logic,  which,  though  they  do  not  properly 
belong  to  the  science  itself,  yet,  as  they  are  generally  dis- 
cussed, often  at  great  length,  in  most  treatises  upon  it,  may 
properly  be  defined  and  explained  here,  while  a  full  consid- 
eration of  them  may  be  regarded  as  an  appendix  to  the 
body  of  the  work.  Properly  speaking,  Pure  Logic  termi- 
nates with  the  consideration  of  the  three  classes  of  prod- 
ucts —  namely,  Concepts,  Judgments,  and  Reasonings  — 
which  are  the  elements  into  which  all  Thought  is  resolved. 
But  Thought  itself  is  subsidiary  to  the  attainment  of  knowl- 
edge, —  that  is,  to  Science.  The  question  remains,  then, 
after  we  have  fully  treated  of  Concepts,  Judgments,  and 
Reasonings,  taken  separately  or  considered  in  themselves 
alone,  what  use  is  to  be  made  of  them,  taken  together, 
in  the  construction  of  Science.  A  full  answer  to  this  ques- 
tion, as  it  would  involve  a  study  of  the  objects  of  Science, 
—  that  is,  of  the  matter  of  the  special  sciences,  —  evidently 
falls  outside  of  the  province  of  Logic.  But  a  partial  answer 
to  it,  regarding  Science  in  its  relation,  not  to  the  objects 
known,  but  to  the  knowing  mind,  may  be  considered  as  a 
natural  appendage  to  Logic,  as  it  embraces  the  conditions 
not  merely  of  possible,  but  of  perfect,  Thought.  Such  an 
answer  is  usually  called  the  Doctrine  of  Method,  or  Logi- 
cal Methodology.  Pure  Logic  considers  only  the  Neces- 
sary Laws  to  which  all  Thought  must  conform  ;  the  Doc- 
trine of  Method  regards  those  rules  and  principles  to  which 
all  Thought  ought  to  conform  in  order  to  obtain  its  end, 
which  is  the  advancement  of  Science.  Pure  Logic  treats 
merely  of  the  elements  of  Thought,  while  Logical  Meth- 
odology regards  the  proper  arrangement  of  these  elements 
into  an  harmonious  whole.  All  Method  is  a  well-defined 
progress  towards  some  end  ;  and  the  end  in  this  case  is  the 
attainment  of  truth.  Practically  speaking,  the  Doctrine 
of  Method  is  a  body  of  rules  or  precepts  looking  to  the 
propyl  regulation  of  the  Thinking  Faculty  in  the  pursuit 


DIVISIONS   OF   THE  SCIENCE.  37 

of  knowledge  ;  and,  as  such,  it  necessarily  lacks  the  pre- 
cision and  the  demonstrative  certainty  which  are  character- 
istic of  the  principles  of  Pure  Logic.  The  Laws  of  Pure 
Thought  are  absolute ;  the  merits  of  Perfect  Thought  are 
various,  and  attainable  in  different  degrees,  according  to 
circumstances. 

Another  distinction  has  been  taken,  in  this  science,  be- 
tween Pure  and  Applied  Logic,  or,  as  Sir  William  Hamil- 
ton prefers  to  call  the  latter,  Modified  Logic.  The  former, 
as  we  have  seen,  considers  the  Thinking  Faculty  alone,  as 
if  it  constituted  the  whole  of  the  human  mind,  and  there- 
fore as  if  its  Laws  and  Products  were  unaffected  by  any 
collateral  and  disturbing  influences,  but  were  manifested  in 
precisely  the  same  manner  by  different  persons.  It  takes 
no  account  of  the  defects  and  hinderances  which  obstruct 
the  normal  action  of  the  understanding.  Modified  Logic, 
on  the  other  hand,  considers  Thought  as  it  is,  and  not 
merely  as  it  ought  to  be.  It  regards  "  the  Causes  of  Error 
and  the  Impediments  to  Truth  by  which  man  is  beset  in 
the  employment  of  his  Faculties,  and  what  are  the  means 
of  their  removal."  And  yet  it  is  a  universal  science,  —  as 
much  so  as  Pure  Logic  ;  —  for  it  does  not  consider  the  Mat- 
ter of  Thought.  The  obstacles  and  imperfections  which  it 
points  out  are  not  those  which  arise  from  the  objects  of  in- 
quiry, but  from  the  inquiring  mind.  They  are  subjective 
or  psychological  causes  of  error.  Lord  Bacon  is  probably 
the  first  philosopher  who  attempted  a  systematic  enumera- 
tion of  the  causes  of  error.  He  made  a  quaint  classification 
of  them,  under  the  significant  name  of  Idols,  into  the  four 
genera  of  Idols  of  the  Tribe,  or  the  necessary  faults  and 
imperfections  of  the  human  intellect  itself;  Idols  of  the 
Den,  which  arise  from  the  special  constitution,  education, 
and  habits  of  each  individual  man ;  Idols  of  the  Forum, 
proceeding  from  the  defects  of  the  language  which  we  are 
obliged  to  employ  as  an  instrument  of  The  ught  and  a  means 


58  DEFINITION   OF  LOGIC. 

of  communication  ;  and  Idols  of  the  Theatre,  or  the  various 
dogmas  of  ill-founded  systems  of  philosophy  which  have 
found  their  way  into  men's  minds  through  tradition,  negli- 
gence, and  credulity. 

But  Modified  Logic  is  not  properly  called  Logic,  as  it  is 
a  branch  of  Psychology,  which  treats  of  the  phenomena  of 
mind  in  general,  and  not  merely  of  the  normal  action  and 
necessary  laws  of  one  special  faculty,  the  Understanding. 
As  Modified  Logic,  however,  is  nearly  allied  in  purpose 
with  the  Doctrine  of  Method,  both  looking  to  the  same 
general  end,  —  the  attainment  of  truth  through  the  proper 
regulation  of  the  Thinking  Faculty,  —  the  two  may  well 
be  considered  together,  under  the  general  name  of  Applied 
Logic,  as  a  kind  of  supplement  to  the  science  properly  so 
called.  Moreover,  the  connection  between  Thought  and 
Language  being  so  intimate,  as  we  have  seen,  that  neither 
can  exist  without  the  other,  it  would  be  an  injurious,  and, 
in  fact,  an  impossible  refinement,  in  a  Treatise  on  Logic,  to 
try  to  avoid  frequent  reference  to  those  mistakes  in  thinking 
which  proceed  from  an  incautious  use  of  words. 

The  utility  of  the  study  of  Logic  —  at  least,  of  Formal 
Logic  —  has  been,  perhaps,  more  generally  doubted  or  de- 
nied, during  the  last  two  or  three  centuries,  than  that  of 
any  other  recognized  science.  In  England  especially,  ever 
since  Bacon's  time,  but  more  particularly  since  that  of 
John  Locke,  the  study  has  been  as  unreasonably  decried  as 
it  was,  during  an  earlier  period,  unduly  exalted.  The 
popular  voice  has  been  against  it,  and,  till  within  the  last 
thirty  years,  it  steadily  lost  ground  even  in  the  Universities, 
where  the  popular  voice  is  not  often  heard  or  respected. 
This  unjust  depreciation  of  the  study  was  due  in  great  part 
to  the  extravagant  pretensions  formerly  put  forward  in  its 
favor.  An  age  which  acknowledged  Bacon  and  Descartes 
to  be  its  intellectual  leaders  was  likely  to  scrutinize  with 
extreme  ^nlousy  the  claims  of  a  science  long  held  forth  by 


UTILITY   OF   THE   STUDY.  39 

its  votaries  as  the  science  or  art  "  of  the  right  use  of  rea- 
son," or  "  of  forming  instruments  for  the  direction  of  the 
mind  " ;  as  "  the  head  and  culminating  point  of  philosophy," 
"  the  art  of  thinking,"  "  the  medicine  of  the  mind,"  "  the 
lighthouse  of  the  intellect,"  "  ars  artium  et  scientia  scienti- 
arum,  qua  aperta,  omnes  aliai  aperiuntur,  et  qua  clausa, 
omnes  alice  clauduntur."  Especially  was  this  the  case,  as  a 
dark  shade  had  already  been  cast  upon  this  boastful  study 
by  the  rapid  decline  and  visibly  approaching  extinction  of 
those  systems  of  philosophy,  theology,  and  physical  science 
which  acknowledged  the  same  parentage,  and  had  long 
been  associated  with  it  in  asserted  pre-eminence  and  ex- 
clusiveness. 

Logic  fared  not  much  better  in  the  hands  of  those,  its 
later  disciples,  who  abated  the  extravagance  of  its  preten- 
sions, indeed,  and,  by  throwing  aside  many  of  its  technicali- 
ties and  nice  distinctions,  rendered  its  aspect  less  abstruse 
and  forbidding.  But,  still  adhering  to  the  opinion  that  its 
main  purpose  was  to  furnish  practical  rules  for  the  guid- 
ance of  the  understanding  in  the  search  after  truth,  they 
destroyed  its  unity,  broke  down  the  boundaries  which  sepa- 
rate it  from  Psychology,  Grammar,  and  Metaphysics,  and 
encumbered  it  with  a  mass  of  disciplinary  precepts  which 
would  be  out  of  place  anywhere  but  in  treatises  on  practi- 
cal education.  The  authors  of  the  excellent  "Art  of  Think- 
ing," which  commonly  passes  under  the  name  of  the  "  Port- 
Royal  Logic,"  deemed  it  necessary  to  apologize  even  for 
the  limited  space  which  they  had  devoted  to  the  special 
doctrines  of  this  science,  on  the  ground  that  "  custom  has 
introduced  a  sort  of  necessity  of  having  at  least  a  slight 
knowledge  of  Logic " ;  and  they  remarked,  that,  as  the 
heads  of  chapters  sufficiently  indicated  the  topics  considered 
in  them,  those  of  exclusively  logical  import  might  De  omit- 
ted in  the  perusal  without  serious  injury  to  what  remained. 
"When  we  thought  any  matter  might  be   of  service  in 


40  DEFINITION   OF  LOGIC. 

forming  the  judgment,"  they  added,  "we  never  scrupled 
to  insert  it,  to  whatever  science  it  might  belong  " ;  and, 
accordingly,  "  in  this  Treatise,  the  reader  will  find  many 
things  relating  to  Physics  and  Ethics,  [still  more,  they 
should  have  added,  belonging  to  Grammar,]  and  almost  as 
much  Metaphysics  as  it  is  necessary  to  know."  This  is 
equivalent  to  denying  that  Logic  has  any  claims  to  be  con- 
sidered as  a  distinct  science,  or  that  a  thorough  and  sys- 
tematic evolution  of  its  principles  would  be  of  any  practical 
benefit. 

The  ground  of  these  misapprehensions  is  entirely  re- 
moved by  the  view  which  has  here  been  given  of  the 
province  and  the  purpose  of  Logic.  Its  boundaries  are 
clearly  defined,  its  pretensions  are  moderate,  and  it  accom- 
plishes all  that  it  is  intended  to  perform.  As  a  Formal 
Science,  it  takes  no  account  of  the  Matter  of  Thought, 
which  is  all  derived  from  processes  of  observation  or  intui- 
tion that  lie  beyond  its  province.  It  is  not  concerned  with 
the  something  that  is  known,  but  only  with  the  manner  of 
knowing  it.  It  is  not  an  organon  of  discoveiy,  then,  or  a 
means  to  be  used  for  the  extension  of  any  science.  It  ana- 
lyzes the  Laws  of  Thought ;  but,  as  these  Laws  are  neces- 
sary and  universal,  —  that  is,  as  they  exist  in  full  force  even 
in  the  humblest  and  least-instructed  intellect,  —  it  does  not 
profess  to  teach  anything  absolutely  new,  but  only  to  bring 
out  into  distinct  consciousness  and  scientific  arrangement 
what  exists  or  takes  place  implicitly  in  every  mind.  These 
Laws  of  Thought  exist  there  in  a  latent  or  involved  form  ; 
and  we  follow  their  guidance  unconsciously,  just  as  a  person 
who  has  learned  to  speak  and  write  only  by  moving  in  good 
society,  and  following  the  example  of  others,  uses  language 
in  strict  conformity  with  grammatical  laws,  though  he  is 
unacquainted  with  these  laws  even  by  name.  The  test  of 
the  validity  of  any  doctrine  in  logical  science  is,  that  those 
to  whom  it  is  now  for  the  first  time  communicated  imme- 


UTILITY   OF  THE   STUDY.  41 

diately  recognize  it  as  nothing  new,  except  in  the  form  of 
statement,  but  as  a  principle  to  which  they  have  always 
conformed  ever  since  they  began  to  think.  The  purpose 
of  Logic,  then,  is  only  to  teach  us  how  we  always  have 
thought,  and  not  any  new  mode  of  thinking,  or  new  pre- 
cautions, through  which  we  may  avoid  the  errors  to  which 
we  were  formerly  liable,  or  by  which  we  may  discover 
truths  that  were  formerly  unattainable.  It  has  no  counsels 
to  give,  except  to  urge  careful  and  uniform  compliance  with 
Laws  which  every  one  admits  to  be  authoritative  and  uni- 
versal, and  to  which  he  has  always  intended  to  conform. 
As  Mr.  Mansel  remarks,  the  science  advises  only  the  better 
performance  of  existing  obligations,  and  does  not  attempt 
the  imposition  of  new  ones.  "A  treatise  on  Logic  is  not 
designed  primarily  to  give  men  facility  in  the  practice  of 
reasoning,  any  more  than  a  treatise  on  Optics  is  intended 
to  improve  their  sight;  and  it  would  be  as  correct  for  a 
writer  on  the  mathematical  principles  of  Optics  to  entitle 
his  work  *  Optics,  or  the  Art  of  improving  defective  Vision,' 
as  it  is  for  a  writer  on  the  principles  of  Logic  to  adopt  for 
his  title,  4  Logic,  or  the  Art  of  Reasoning.'  "  * 

Indirectly,  indeed,  the  science  may  be  regarded  as  a 
medicine  of  the  mind.  As  it  brings  out  into  clearer  con- 
sciousness the  laws  to  which  all  just  thinking  must  conform, 
the  indistinctness  and  confusion  of  thought  to  which  we  are 
all  liable  are  dissipated,  and  the  errors  which  often  follow 
the  symbolic  use  of  language,  or  the  substitution  of  words 
for  thought,  are  exposed  and  eliminated.  In  these  respects, 
we  think  rightly  as  soon  as  we  have  learned  to  think  clear- 
ly ;  for  the  necessary  forms  of  the  understanding  govern 
without  dispute,  when  their  applicability  to  the  case  in  hand 
has  become  manifest.  "  The  progress  of  the  sciences," 
says  Hamilton,  "  consists,  not  merely  in  the  accumulation 
cf  new  matter,  but  likewise  in  the  detection  of  the  relations 
*  Introduction  to  Aldrich's  Logic,  third  edition,  p.  lvii 


42  DEFINITION   OF  LOGIC. 

subsisting  among  the  materials  accumulated ;  and  the  re- 
flective abstraction  by  which  this  is  effected  must  not  only 
follow  the  laws  of  Logic,  but  is  most  powerfully  cultivated 
by  the  habits  of  logical  study.''  As  we  spread  out  Con- 
cepts into  their  constituent  Intuitions,  or  individualize  them 
in  particular  Imaginations,  their  true  relations  to  each  are 
intuitively  perceived,  and  inconsequence  or  contradiction  in 
uniting  them  becomes  impossible.  All  this,  however,  is 
but  the  elimination  of  Formal  error ;  the  Matter  of  thought 
comes  from  other  sources ;  and  for  the  mistakes  which  arise 
from  limited  observation,  or  imperfect  induction,  Logic  has 
no  remedy  to  offer.  It  guarantees  the  correctness  neither 
of  the  premises  nor  of  the  conclusion,  but  only  the  validity 
of  the  inference  from  the  former  to  the  latter.  Hence, 
what  is  formally  correct  may  be  materially  false  ;  I  may 
reason  rightly  from  wrong  premises  to  a  false  conclusion. 
On  the  other  hand,  as  an  error  in  the  Form  necessarily 
vitiates  the  whole  process  of  Thought,  it  may  certainly  be 
said  that  Logic  furnishes  us  with  a  negative  criterion  be- 
tween truth  and  falsehood.  The  blunders  which  it  exposes 
are  vital,  but  they  are  not  those  which  are  most  insidious, 
or  even  of  the  most  frequent  occurrence. 

Truth  is  the  agreement  of  a  cognition  with  the  object 
which  it  is  intended  to  represent.  Now  Logic,  as  it  takes 
no  cognizance  of  the  object,  which  is  the  Matter  of  Thought, 
is  evidently  incompetent  to  determine  whether  such  agree- 
ment exists  or  not.  But  there  is  a  preliminary  question  to 
be  settled  before  we  come  to  a  consideration  of  the  object ; 
we  inquire  whether  the  cognition  agrees  with  itself,  —  that 
is,  whether  it  is  Formally  correct.  And  this  question  Logic 
is  competent  to  determine  with  absolute  certainty.  The 
Formal  correctness  of  a  cognition  does  not  by  any  means 
insure  its  Material  truth ;  but  as  Kant  remarks,  it  is  to  be 
regarded  as  a  conditio  sine  qua  non  of  such  truth. 

The  high  place  which  Logic  once  held  among  the    roper 


UTILITY   OF   THE   STUDY.  43 

studies  of  a  University,  and  which  within  a  few  years  it  has 
wellnigh  reclaimed,  is  vindicated  by  the  great  value  of  the 
effort  which  is  necessary  to  master  it,  considered  simply  as  a 
vigorous  exercise  of  the  understanding.  Indeed,  its  chief 
function  is  disciplinary,  for  the  effort  to  acquire  it  may  be 
said  to  equal  or  surpass  in  value  the  subsequent  use  to  be 
made  of  the  acquisition.  It  is  not  of  so  much  importance 
to  know,  as  it  is  to  have  strengthened  and  developed  all  the 
faculties  in  learning  to  know.  No  other  study  taxes  so 
severely  the  power  of  abstract  thought,  and  hence  no  one 
furnishes  better  preparatory  training  for  the  pursuit  of  all 
the  sciences  which  do  not  consist  mainly  in  accumulating 
facts  and  registering  the  materials  thus  obtained. 

Little  needs  to  be  said  of  the  intrinsic  dignity  of  the  sub- 
ject. "  Admitting,"  says  Heinrich  Richter,  as  translated  by 
Hamilton,  "  that  this  science  teaches  nothing  new,  that  it 
neither  extends  the  boundaries  of  knowledge,  nor  unfolds 
the  mysteries  which  lie  beyond  the  compass  of  our  reflective 
intellect,  and  that  it  only  investigates  the  immutable  laws 
to  which  the  mind  in  thinking  is  subjected,  still,  inasmuch 
as  it  develops  the  application  of  these  laws,  it  bestows  on 
us,  to  a  certain  extent,  a  dominion  over  our  thoughts  them- 
selves. And  is  it  nothing  to  watch  the  secret  workshop  in 
which  nature  fabricates  cognitions  and  thoughts,  and  to 
penetrate  into  the  sanctuary  of  self-consciousness,  to  the  end 
that,  having  learnt  to  know  ourselves,  we  may  be  qualified 
rightly  to  understand  all  else  ?  Is  it  nothing  to  seize  the 
helm  of  thought,  and  to  be  able  to  turn  it  at  our  will  ?  For 
through  a  research  into  the  laws  of  thinking,  Logic  gives 
us,  in  a  certain  sense,  a  possession  of  the  thoughts  them- 
selves. It  is  true,  indeed,  that  the  mind  of  man  is,  like  the 
universe  of  matter,  governed  by  eternal  laws,  and  follows, 
even  without  consciousness,  the  invariable  canons  of  its  na- 
ture. But  to  know  and  understand  itself,  and  out  of  the 
boundless  chaos  of  phenomena  presented  to  the  senses  to 


44  DEFINITION   OF   LOGIC. 

form  Concepts,  through  Concepts  to  reduce  that  chaos  to 
harmony  and  arrangement,  and  thus  to  establish  the  domin- 
ion of  intelligence  over  the  universe  of  existence,  —  it  is 
this  alone  which  constitutes  man's  grand  and  distinctive 
pre-eminence."  "  Oui  whole  dignity,"  says  Pascal,  "  con- 
sists in  thought." 

It  is  also  argued  by  Sir  William  Hamilton,  with  great 
force,  that  "  Logic  is  further  useful  as  affording  a  Nomen- 
clature of  the  laws  by  which  legitimate  thinking  is  governed, 
and  of  the  violation  of  these  laws,  through  which  thought 
becomes  vicious  or  null. 

"  It  is  said,  in  Hudibras,  — 

'  That  all  a  Rhetorician's  rules, 
Serve  only  but  to  name  his  tools ' ; 

and  it  may  be  safely  confessed  that  this  is  one  of  the  prin- 
cipal utilities  of  Rhetoric.  A  mere  knowledge  of  the  rule* 
of  Rhetoric  can  no  more  enable  us  to  compose  well,  than  a 
mere  knowledge  of  the  rules  of  Logic  can  enable  us  to 
think  well.  There  is  required  from  nature,  in  both,  the 
faculty  ;  but  this  faculty  must,  in  both  departments,  be  cul- 
tivated by  an  assiduous  and  also  a  well-directed  exercise ; 
that  is,  in  the  one,  the  powers  of  Comparison  must  be  exer- 
cised according  to  the  rules  of  a  sound  Rhetoric,  in  the 
other,  according  to  the  rules  of  a  sound  Logic.  In  so  far, 
therefore,  the  utility  of  either  science  is  something  more 
than  a  mere  naming  of  their  tools.  But  the  naming  of 
their  tools,  though  in  itself  of  little  value,  is  valuable  as  the 
condition  of  an  important  function,  which,  without  this, 
could  not  be  performed.  "Words  do  not  give  thoughts  ;  but 
without  words,  thoughts  could  not  be  fixed,  limited,  and 
expressed.  They  are,  therefore,  in  general,  the  essential 
condition  of  all  thinking  worthy  of  the  name.  Now,  what 
is  true  of  human  thought  in  general,  is  true  of  Logic  and 
Rhetoric  in  particular.    The  nomenclature  in  these  sciences 


UTILITY   OF   THE   STUDY.  4d 

is  the  nomenclature  of  certain  general  analyses  and  distinc- 
tions, which  express  to  the  initiated,  in  a  single  word,  what 
the  uninitiated  could  (supposing  —  what  is  not  probable  — 
that  he  could  perform  the  relative  processes)  neither  under- 
stand nor  express  without  a  tedious  and  vague  periphrasis ; 
while,  in  his  hands,  it  would  assume  only  the  appearance 
of  a  particular  observation,  instead  of  a  particular  instance 
of  a  general  and  acknowledged  rule.  To  take  a  very  sim- 
ple example  :  —  there  is  in  Logic  a  certain  sophism,  or  act 
of  illegal  inference,  by  which  two  things  are,  perhaps  in  a 
very  concealed  and  circuitous  manner,  made  to  prove  each 
other.  Now,  the  man  unacquainted  with  Logic  may  per- 
haps detect  and  be  convinced  of  the  fallacy ;  but  how  will 
he  expose  it  ?  He  must  enter  upon  a  long  statement  and 
explanation,  and,  after  much  labor  to  himself  and  others,  he 
probably  does  not  make  his  objection  clear  and  demonstra- 
tive after  all.  But  between  those  acquainted  with  Logic, 
the  whole  matter  would  be  settled  in  two  words.  It  would 
be  enough  to  say  and  show,  that  the  inference  in  question 
involved  a  circulus  in  concludendo,  and  the  refutation  is  at 
once  understood  and  admitted.  It  is  in  like  manner  that 
one  lawyer  will  express  to  another  the  ratio  decidendi  of  a 
case  in  a  single  technical  expression  ;  while  their  clients  will 
only  perplex  themselves  and  others  in  their  attempts  to  set 
forth  the  merits  of  their  cause.  Now,  if  Logic  did  nothing 
more  than  establish  a  certain  number  of  decided  and  deci- 
sive rules  in  reasoning,  and  afford  us  brief  and  precise 
expressions  by  which  to  bring  particular  cases  under  these 
general  rules,  it  would  confer  on  all  who  in  any  way  employ 
their  intellect  —  that  is,  on  the  cultivators  of  every  human 
science  —  the  most  important  obligation.  For  it  is  only  in 
the  possession  of  such  established  rules,  and  of  such  a  tech- 
nical nomenclature,  that  we  can  accomplish,  with  facility, 
and  to  an  adequate  extent,  a  criticism  of  any  work  of  rea- 
soning.    Logical  language  is  thus,  to  the  general  reasoner, 


46  DEFINITION   OF  LOGIC. 

what  the  notation  of  Arithmetic,  and  still  more  of  Algebra, 
is  to  the  mathematician.  Both  enable  us  to  comprehend 
and  express,  in  a  few  significant  symbols,  what  would  other- 
wise overpower  us  by  their  complexity ;  and  thus  it  is,  that 
nothing  would  contribute  more  to  facilitate  and  extend  the 
faculty  of  reasoning,  than  a  general  acquaintance  with  the 
rules  and  language  of  Logic,  —  an  advantage  extending  in 
deed  to  every  department  of  knowledge,  but  more  especially 
of  importance  to  those  professions  which  are  occupied  in 
inference,  and  conversant  with  abstract  matter,  such  as  The 
ology  and  Law." 


THE   PRIMARY   AXIOMS   OF   PURE   THOUGHT. 

TJST  SITT 

CHAPTER    III. 

THE  PRIMARY  AXIOMS  OF  PURE  THOUGHT. 

HAVING  defined  Logic  to  be  the  Science  of  the  Neces- 
sary Laws  of  Pure  Thought,  our  first  object  must  be 
to  ascertain  what  are  the  Fundamental  and  Universal  Laws, 
here  called  Primary  Axioms,  to  which  all  Thought,  as  such, 
is  subject.  In  the  separate  consideration,  which  will  come 
afterwards,  of  the  three  classes  of  Thoughts,  —  namely, 
Concepts,  Judgments,  and  Reasonings,  —  we  may  expect 
to  find  Special  Laws  or  Rules  which  are  applicable  only  to 
one  or  two  of  these  divisions.  Such  Special  Rules  may  or 
may  not  be  derivative  in  character;  —  that  is,  they  may 
be  either  immediate  inferences  from  the  Primary  Axioms 
which  govern  all  the  products  of  the  Thinking  Faculty,  or 
they  may  be  independent,  as  resting  upon  their  own  evi- 
dence. Of  this  hereafter.  But  our  first  inquiry  must  be, 
whether  there  are  any  Axioms  of  universal  applicability, 
which  underlie  and  govern  every  act  and  product  of  the 
human  Understanding ;  and,  if  there  are  such,  to  deter- 
mine their  character  and  significance. 

If  there  are  such  Axioms,  they  must  be  few,  meagre  in 
import,  not  susceptible  of  proof,  and  recognizable  by  all  as 
familiar  truisms,  which  have  always  implicitly  directed  their 
thoughts,  though  perhaps,  on  account  of  their  very  obvi- 
ousness, they  have  never  been  explicitly  stated  or  drawn 
out  into  distinct  consciousness.  They  must  have  these 
characteristics,  because  they  concern  only  the  Forms  of 
Thought,  or  the  manner  of  thinking  irrespective  of  what 


48  THE' PRIMARY   AXIOMS   OF   PURE   THOUGHT. 

we  are  thinking  about ;  and  as  these  Forms  themselves  are 
necessarily  limited  in  number  and  narrow  in  significance, 
the  Axioms  which  underlie  them  all,  and  constitute  their 
common  features,  must  be  still  fewer  and  poorer  in  import. 
They  cannot  admit  of  proof,  as  their  truth  is  presupposed 
in  every  act  of  reasoning,  and  therefore  no  argument  or 
proof  is  possible  unless  their  veracity  is  taken  for  granted. 
They  must  be  recognized  by  all  as  mere  truisms,  because 
they  are  thus  self-evident,  and  because  their  truth  has  been 
acknowledged  and  acted  upon  in  every  Form  of  Thought 
which  we  have  ever  experienced.  The  First  Principles  of 
all  the  sciences  are  avowedly  thus  few  and  meagre,  as  is 
seen  to  be  the  case  with  the  introductory  axioms  of  Geome- 
try and  Physics.  With  still  more  reason  do  we  expect  the 
First  Principles  of  all  Thought  to  possess  this  character,  as 
they  stand  in  the  same  relation  to  the  axioms  of  the  special 
sciences,  that  these  axioms  do  to  the  most  advanced  theo- 
rems which  have  been  built  upon  them,  or  which  have  been 
constructed  by  taking  them  for  granted. 

After  tins  explanation,  we  need  not  be  surprised  to  find 
that  all  the  Primary  Axioms  of  Pure  Thought  are  perhaps 
reducible  to  this  single  principle :  —  All  Thought  must  be 
consistent  ivith  itself.  If  it  be  inconsistent,  —  if,  directly  or 
indirectly,  it  contradicts  itself,  —  it  is  self-destructive,  and 
the  Thought  is  null.  Thus  stated,  the  principle  is  coinci- 
dent with  that  which  is  usually  called  the  Law  of  Contra- 
diction, though,  as  Hamilton  remarks,  it  ought  rather  to  be 
termed  the  Law  of  Non-Contradiction.  Practically  speak- 
ing, eveiy  Thought  which  must  be  rejected  as  formally 
invalid  —  that  is,  which  is  radically  vicious  in  Form,  what- 
ever be  its  Matter  —  offends  against  this  principle.  By 
logicians  generally,  however,  this  principle  has  been  expli- 
cated into  three  general  Axioms,  called  the  Law  of  Identity, 
the  Law  of  Contradiction,  and  the  Law  of  Excluded  Middle. 
The  ground  of  this  explication  may  be  thus  set  forth. 


THE   PRIMARY   AXIOMS   OF   PURE   THOUGHT.  49 

The  primary  element  of  all  Thought  is  a  Judgment, 
which  arises  from  a  Comparison.  Hence,  all  Thought 
must  proceed  either  by  affirmation  or  denial,  as  these  are 
the  only  two  possible  forms  of  Judgment.  Having  com- 
pared any  two  Concepts  with  each%ther,  we  either  perceive 
their  identity,  similarity,  congruence,  or  some  other  relation 
whereby  we  affirm  their  union  in  one  act  of  Thought ;  or 
we  perceive  the  opposite  relation  between  them,  such  as 
difference,  unlikeness,  or  incompatibility,  whereby  we  deny 
one  of  the  other.  As  any  Concept  can  be  compared  with 
any  other,  and  as  the  Judgment  which  follows  such  com- 
parison must  either  affirm  or  deny  one  of  the  other,  there 
being  no  third  form  of  Judgment  conceivable,  we  have  the 
Axiom  which  is  usually  called  the  Law  of  Excluded  Third 
or  Excluded  Middle,  —  Lex  Exclusi  Tertii  aut  Medii. 
Either  A  is  B,  or  A  is  not  B :  if  we  make  any  Judg- 
ment, < —  that  is,  if  we  think  at  all,  —  one  of  these  two 
must  be  true  ;  for  no  third  form  is  conceivable.  It  has 
been  enounced  in  various  forms :  —  Of  two  contradictory 
judgments,  one  must  be  true ;  Every  predicate  may  be 
affirmed  or  denied  of  every  subject ;  Every  conceivable 
thing  is  either  A  or  not-A.  Of  course,  A  and  not-A,  taken 
together,  include  the  universe,  —  the  universe  not  only  of 
all  that  is  actual,  but  of  all  that  is  conceivable ;  for  as  not-A 
excludes  A  only  and  nothing  else,  it  includes  the  universe 
excepting  A  only. 

Still  further :  —  Not  only  are  affirmation  and  negation  the 
only  conceivable  forms  of  Judgment,  but,  as  contradictory 
opposites,  they  are  absolutely  incompatible  or  mutually 
destructive.  The  admission  of  one  is  tantamount  to  a 
rejection  of  the  other.  If  taken  together,  they  destroy 
each  other,  and  the  Thought  is  rendered  null.  We  can- 
not affirm  both  A  and  not-A  of  the  same  thing.  Here  we 
have  the  well-known  Law  of  Contradiction,  more  properlv  of 
Non-Contradiction,  of  which  the  formula  is,  A  is  not  not-A, 


50  THE   PRIMARY   AXIOMS   OF   PURE   THOUGHT. 

Evidently  this  Law  is  the  principle  of  all  logical  negation 
and  discrimination.  It  has  been  variously  expressed:  — 
Contradictory  attributes  cannot  be  affirmed  of  the  same 
subject ;  What  is  contradictory  is  inconceivable.  It  is  less 
correctly  expressed  in  tlfe  adage,  "  It  is  impossible  for  the 
same  thing  to  be  and  not  to  be."  This  is  a  maxim  which 
concerns  the  Matter  of  Thought,  and  therefore  we  must 
add  to  it  the  material  limitations,  in  the  same  place,  at  the 
same  time,  in  the  same  respect,  &c.  It  is  a  mistake,  then,  to 
maintain  that  the  Axiom,  "  Contradictory  attributes  cannot 
be  affirmed  of  the  same  subject,"  is  not  universally  true,  be- 
cause we  can  form  such  assertions  as  this :  A  man  can  be 
both  young  arid  not-young,  tJiough  not  at  the  same  time.  In 
Logic,  where  we  consider  only  the  Form  of  the  Thought, 
a  Judgment  must  be  expressed  by  the  present  tense  of  the 
verb  to  be;  for  what  we  affirm  is  not  the  past  or  future 
union  of  two  real  phenomena,  but  the  present  coexistence 
and  agreement  of  two  Concepts  in  the  mind.  Hence,  the 
logical  Judgment,  this  man  is  not  young,  is  absolutely 
incompatible  with  the  assertion,  this  man  is  young,  though 
it  is  compatible  with  the  very  different  assertion,  this  man 
has  been  young. 

Once  more :  The  formula,  A  is  not  not-A,  proves,  on 
reduction,  to  be  the  exact  equivalent  or  consequence  of 
this,  A  is  A.  Here  we  have  the  principle  of  affirmation 
and  agreement,  as  the  former  was  that  of  negation  and  dif- 
ference. If  an  object  cannot  be  thought  under  contradic- 
tory attributes,  it  is  because  it  has  a  definite  character  of 
its  own,  excluding  one  of  the  contradictories  through  in- 
cluding the  other.  "  The  universe  of  conceivable  objects," 
to  adopt  Mr.  Mansel's  language,  "embraces  both  A  and 
not-A  ;  it  is  only  when  definitely  conceived  as  the  one,  that 
an  object  cannot  be  conceived  as  the  other.  Every  object 
of  thought,  as  such,  is  thus  conceived  by  limitation  and 
difference  ;  as  having  definite  characteristics  by  which  it  ii 


THE  PRIMARY  AXIOMS  QF  PURE  THOUGHT.      51 

marked  off  and  distinguished  from  all  others ;  as  being,  in 
short,  itself,  and  nothing  else."  Here,  then,  we  have  a 
third  Primary  Axiom,  expressed  as  the  Law  of  Identity : 
Every  A  is  A  ;  Every  object  of  thought  is  conceived  as 
itself;  Every  thing  is  equal  to  itself  or  agrees  with  itself; 
Every  whole  is  the  sum  of  all  its  parts. 

Thus  we  have  three  Primary  Axioms  of  Pure  Thought, 
—  the  Law  of  Identity,  the  Law  of  Contradiction,  and  the 
Law  of  Excluded  Middle,  —  all  of  which  may  be  regarded  as 
explications  of  the  single  rule,  that  all  Thought  must  be  con- 
sistent with  itself,  or  as  corollaries  from  this  one  principle, 
that  Judgment,  which  is  the  basis  of  all  Thought,  proceeds 
only  by  affirmation  and  denial.  The  mutual  dependence 
and  correlation  of  these  three  Axioms  may  be  further  illus- 
trated thus. 

I  can  think  any  object  only  by  placing  it  under  a  Con- 
cept, or  Class-notion  expressed  by  a  General  Term ;  and  I 
can  do  this  only  by  recognizing  that  it  possesses  the  attri- 
butes which  belong  to  this  Concept  and  are  common  to  all 
the  members  of  this  Class  (Law  of  Identity,  affirmation  of 
similarity  or  agreement)  ;  by  discriminating  it  from  other 
objects  which  have  different  attributes  (Law  of  Contradic- 
tion, negation  of  agreement)  ;  and  both  this  affirmation  and 
denial  proceed  by  the  Law  of  Excluded  Middle,  which  de- 
clares, for  each  given  attribute,  that  the  one  or  the  other  is 
absolutely  necessary.  Either  it  does,  or  does  not,  belong  to 
the  object,  and  the  object  does  or  does  not  belong  to  the 
Class.  In  respect  to  the  Laws  of  Identity  and  Contradic- 
tion, says  Sir  William  Hamilton,  "  each  infers  the  other, 
but  only  through  the  principle  of  Excluded  Middle ;  and 
the  principle  of  Excluded  Middle  only  exists  through  the 
supposition  of  the  two  others.  Thus,  the  principles  of 
Identity  and  Contradiction  cannot  move,  —  cannot  be  ap- 
plied, —  except  through  supposing  the  principle  of  Excluded 
Middle ;  and  this  last  cannot  be  conceived  existent  except 


52  THE   PRIMARY   AXIOMS   OF   PURE   THOUGHT. 

through  the  supposition  of  the  two  former.  They  are  thus 
coordinate,  but  inseparable.  Begin  with  any  one,  the  other 
two  follow  as  corollaries." 

Hence  he  symbolizes  the  three  Axioms  by  a  Triangle, 
thus :  — 


C  is  either  r  or  non-I". 


These  three  Axioms  are  sufficient  for  all  purposes  of  ana- 
lytic Thought.  There  is,  however,  another  large  class  of 
Judgments,  which  are  dependent  in  part  upon  a  fourth  Ax- 
iom ;  and,  as  a  preliminary  to  the  consideration  of  it,  we 
must  explain  the  difference  between  analytic  and  synthetic 
Thought.  Kant  was  the  first  to  bring  this  distinction  into 
notice  as  one  of  great  importance  in  philosophy. 

In  an  analytic  Judgment,  the  Predicate  affirms  nothing 
which  was  not  already,  though  implicitly,  contained  in  the 
Concept  which  forms  the  Subject.  We  analyze  a  Concept 
into  the  Marks  or  attributes  of  which  it  consists,  and  then 
pi  edicate  of  it  one  or  more  of  these  Marks.  Of  course,  no 
oi  her  knowledge  is  requisite  for  forming  such  a  Judgment 
than  is  already  contained  in  the  Subject  itself,  as  the  Predi- 
cate affirms  nothing  more  than  what  is  so  contained.  Thus, 
if  I  say,  Body  is  extended,  A  circle  is  round,  An  equilateral 
triangle  has  three  equal  sides,  I  merely  repeat,  or  state 
explicitly,  what  is  already  implied  in  the  very  notion  of  a 
fady,  a  circle,  and  an  equilateral  triangle.     But  in  the  prop- 


TH£   PRIMARY    AXIOMS   OF   PURE   THOUGHT.  58 

ositions,  Body  is  heavy,  A  circle  is  a  particular  section  of  a 
cone,  A  triangle  is  a  figure  the  three  angles  of  which  are 
equal  to  two  right  angles,  the  Predicate  adds  something  that 
was  not  previously  known  and  included  in  the  notion  of  the 
Subject.  There  must  be  some  reason  for  such  addition  ; 
otherwise,  all  Thought  which  is  not  merely  analytical  in 
character  would  be  arbitrary  and  inconsequent.  Pure 
Thought,  which  deals  only  with  the  Form,  and  not  with 
the  Matter,  of  Thinking,  does  not  ask  what  this  reason  is, 
and  seeks  not  in  any  way  to  determine  its  character.  It 
only  demands  that  there  should  be  some  reason,  —  that  the 
connections  of  Thought,  or  those  reductions  to  unity  in 
which  all  Thinking  consists,  should  not  be  merely  casual  or 
capricious ;  in  which  case,  there  would  be  no  proper  con- 
nection at  all. 

Besides  the  first  postulate  of  the  Understanding,  that  all 
Thought  should  be  consistent  with  itself,  we  have,  then,  this 
second  demand,  in  reference  at  least  to  synthetic  Judg- 
ments, that  all  Thought  should  be  consequent;  that  is,  that 
it  should  never  affirm  or  deny  a  union  of  two  Concepts 
without  any  ground  for  such  affirmation  or  denial.  The 
sufficiency  of  this  ground  or  reason  is  a  material  question, 
with  which  the  logician,  as  such,  has  nothing  to  do.  Leib- 
nitz was  wrong,  then,  in  denominating  this  principle  that 
of  "  the  Sufficient  Reason."  The  limitation  is  superfluous, 
for  the  only  reason  required  is  one  that  will  make  the  union 
of  the  predicate  with  the  subject  conceivable, — not  an  actual 
union  of  real  things ;  and  the  reason  which  is  insufficient 
for  this  end  is  no  reason  at  all.  This  axiom,  which  is  prop- 
erly called  that  of  Reason  and  Consequent,  or  the  Condi- 
tion and  the  Conditioned,  is  expressed  in  the  formula,  affirm 
nothing  without  a  ground  or  reason;  or,  every  affirmation 
must  have  a  ground  or  reason  why  it  is  affirmed. 

As  the  former  postulate  was  evolved  into  three  Axioms, 
so  this  one  may  be  explicated  into  two,  such  explication 


54      THE  PRIMARY  AXIOMS  OF  PURE  THOUGHT. 

being,  in  fact,  only  a  statement  of  the  meaning  of  the  words 
employed.  The  first  of  these  derivative  Axioms  is,  that  to 
affirm  the  Reason  or  the  Condition  is  also  to  affirm  the  Con- 
sequent or  the  Conditioned;  for  the  Reason  would  not  be 
the  Reason  unless  the  Consequent  followed  it.  The  second 
Axiom  is,  that  to  deny  the  Consequent  is  also  to  deny  the 
Reason;  for,  again,  if  the  Consequent  does  not  follow,  the 
Reason  cannot  exist,  since  the  Reason  means  only  that 
which  necessitates  the  Consequent.  The  two  Axioms  are 
thus  pithily  stated  by  the  old  Logicians  :  Positd  conditione 
ponitur  conditionatum,  sublato  conditional  tollitur  conditio  ; 
or  thus :  A  ratione  ad  rationatum,  a  negatione  rationati  ad 
negationem  rationis,  valet  consequentia. 

Observe,  however,  that  the  converse  of  these  two  Axi- 
oms does  not  hold  good.  To  affirm  the  Consequent  is  not 
to  affirm  any  given  Reason,  since  the  Consequent  may  have 
followed  from  some  other  Reason ;  and  the  same  considera- 
tion shows  that  it  is  not  competent,  from  a  denial  of  any 
given  Reason,  to  infer  a  denial  of  the  Consequent.  The 
primary  Axiom  asserts  only  the  necessity  of  some  Reason 
or  other,  not  of  any  one  Reason.  The  explication  may  be 
thus  summed  up  in  a  tabular  form  :  —  . 

There  must  be  a  Ground  or  Reason  for  every  affirmation. 

Affirming  the  Reason  affirms  also  the  Consequent. 

Denying  the  Reason,  nothing  follows. 

Affirming  the  Consequent,  nothing  follows. 
Denying  the  Consequent    denies  also  the  Reason. 

Strictly  speaking,  this  Axiom  is  applicable  to  all  analytic, 
as  well  as  to  all  synthetic  Judgments,  and  therefore,  like 
each  of  the  other  three  Axioms,  it  is  a  Universal  Law  of 
Thought.  But  in  the  case  of  analytic  Judgments  this  Ax- 
iom does  not  need  to  be  separately  considered  or  enounced, 
for  the  ground  or  reason  to  which  it  refers  is  contained  in 


THE  PRIMARY  AXIOMS   OF  PURE  THOUGHT.  55 

the  Judgment  itself ;  we  cannot  think  the  latter  without  the 
former.  Thus,  we  cannot  think  of  body  without  extension  ; 
and  therefore,  when  we  affirm  that  body  is  extended,  the 
Judgment  carries  its  own  reason  or  justification  along  -with 
it.  But  in  synthetic  Thought,  as  when  we  say  that  matter 
is  compressible,  we  see  no  reason  in  the  Thought  itself  why 
the  attribute  of  compressibility  should  be  affirmed  of  it,  any 
more  than  incompressibility.  The  Axiom  of  Excluded  Mid- 
dle tells  us  that  one  or  the  other  must  be  so  predicated,  — 
that  matter  must  be  either  compressible  or  incompressible. 
Another  necessaiy  Law  of  Thought  —  that  of  Reason  and 
Consequent  —  forbids  us  to  predicate  either  of  these  con- 
tradictories to  the  necessary  exclusion  of  the  other,  without 
a  ground  for  such  preference  ;  and  the  reason  in  this  case 
must  be  derived  from  some  source  exterior  to  the  Judgment 
itself,  as  no  analysis  of  the  latter  will  afford  any  such  reason. 
We  may,  indeed,  predicate  neither ;  we  may  leave  the 
Thought,  so  far  as  this  pair  of  contradictories  is  concerned, 
wholly  indeterminate.  But  if  we  affirm  anything  of  it,  be- 
yond what  is  already  contained  in  it,  there  must  be  a  reason, 
express  or  implied,  for  such  affirmation. 

With  obvious  propriety,  analytic  Judgments  are  also 
called  explicative,  as  they  merely  unfold,  and  thereby 
bring  into  clearer  consciousness,  what  we  already  possess. 
By  them  our  knowledge  is  cleared  up  and  rendered  ex- 
plicit, but  is  not  at  all  enlarged.  Synthetic  Judgments,  on 
the  other  hand,  are  properly  called  ampliative,  as  by  them 
our  sum  of  knowledge  is  increased.  Each  of  these  re- 
quires a  reason,  as  otherwise  its  result  would  not  be  the 
enlargement  of  knowledge,  but  the  caprice  of  ignorance. 

It  is  rightly  observed  by  Krug,  that  the  relation  of  Rea- 
son and  Consequent  is  something  different  from  that  of 
Cause  and  Effect.  It  is  true  that  Cause  and  Effect,  so  far 
as  they  are  conceived  in  thought,  stand  to  each  other  as  Rea- 
son and  Consequent.    But  the  converse  is  not  true  ;  all  Rea- 


56      THE  PRIMARY  AXIOMS  OF  PURE  THOUGHT. 

sons  are  not  Causes,  and  all  Consequents  are  not  Effects. 
The  two  relations  may  be  distinguished  from  each  other  ag 
being  respectively  what  the  old  logicians  called  the  ratio 
cognmcendi  and  the  ratio  essendi.  Thus,  to  take  an  exam- 
ple, the  ground  being  wet  is  the  Reason  why  I  know  that  it 
has  rained;  this  is  the  ratio  cognoscendi,  and  it  is  evidently 
a  relation  of  one  thought  to  another  thought;  though  the 
wetness  of  the  ground  is  certainly  not  the  Cause  of  the 
rain,  yet,  because  I  know  that  the  ground  is  wet,  I  am  jus- 
tified in  thinking  that  the  rain  has  fallen.  On  the  other 
hand,  the  falling  of  the  rain  is  the  Cause  of  the  ground 
being  wet ;  this  is  the  ratio  essendi,  and  it  is  the  relation 
of  one  real  thing,  or  actual  occurrence,  to  another ;  and,  as 
such,  it  is  independent  of  any  thought,  as  the  one  thing 
would  still  cause  the  other,  though  there  were  no  mind  to 
observe  their  connection.  Hence,  the  relation  of  Reason 
and  Consequent  is  a  mere  synthesis  of  thoughts ;  the 
thought  of  wetness  of  the  ground  suggests,  and,  so  to 
speak,  justifies  the  thought  of  rain.  But  Cause  and  Effect 
expresses  an  actual  union  of  physical  events,  the  real  exist- 
ence of  the  one  compelling  or  necessitating  the  existence  of 
the  other. 

This  seems  the  proper  place  to  introduce  what  is  called 
"  the  postulate  of  Logic,"  — a  precept  which  Logicians  have 
always  assumed,  and  acted  upon  in  part,  but  which,  before 
Sir  William  Hamilton's  time,  they  never  distinctly  enounced, 
or  carried  out  consistently  in  all  its  consequences.  To  adopt 
his  language,  — 

"  The  only  postulate  of  Logic  which  requires  an  articu- 
late enouncement  is  the  demand,  that,  before  dealing  with  a 
judgment  or  reasoning  expressed  in  language,  the  import  of 
its  terms  should  be  fully  understood  ;  in  other  words,  Logic 
postulates  to  be  allowed  to  state  explicitly  in  language  what 
is  implicitly  contained  in  the  Thought." 

This  assumption  is  grounded  upon  the  two  fundamental 


THE  PRIMARY   AXIOMS   OF   PURE  THOUGHT.  57 

pi  opositions  already  stated  and  explained,  namely,  that 
Logic  deals  only  with  the  Form,  and  not  with  the  Matter, 
of  Thought;  and  that  it  is  concerned  primarily  with  the 
Thought,  and  only  secondarily  with  the  accident  of  its  ex- 
pression. The  science  claims,  therefore,  to  fill  up  the  gaps 
and  elisions  of  ordinary  discourse,  wherein  much  is  sacri- 
ficed to  brevity  of  speech,  and  to  pare  down  the  complexity 
and  redundance  of  rhetorical  expression  into  logical  sim- 
plicity and  precision.  For  ordinary  purposes,  and  for  the 
Rhetorician's  use,  language  is  a  vehicle  for  the  rapid  and 
effective  communication  both  of  Thought  and  feeling ;  con- 
sequently, it  deals  much  in  hints  and  abbreviated  forms  of 
speech,  taking  for  granted  all  that  the  reader's  and  hearer's 
mind  will  readily  supply,  and  aiming  only  to  bring  his  fac- 
ulties of  reasoning,  imagination,  and  emotion  into  play  in 
the  right  direction.  The  Logician,  on  the  other  hand, 
seeks  to  express  nothing  but  Thought;  and  he  aims  to 
make  language  a  perfect  representative  of  the  Thought  in 
its  simplicity  and  entireness.  His  proper  function  is  to 
point  out  those  minute  but  frequently  recurrent  elements 
of  Thought,  which,  precisely  because  frequently  recurrent, 
are  elided  or  passed  over  in  ordinary  discourse.  Of  course, 
the  expressions  which  he  thus  finds  occasion  to  use  will 
often  appear  awkward  and  redundant,  tediously  minute, 
and  even  tautological.  But  he  is  not  responsible  for  their 
rhetorical  demerits ;  the  only  question  for  him  is,  whether 
they  fully  and  correctly  express  all  that  is  actually  passing 
in  Thought.  Thus,  the  common  form  of  argumentation  is 
the  Enthymeme,  which  consists  of  but  two  propositions ; 
but  its  Logical  form  is  the  Syllogism,  consisting  of  three. 
No  one  but  a  silly  pedant  ever  speaks  or  writes  Syllogisms, 
except  in  a  treatise  on  Logic.  But  the  only  question  is, 
whether  everybody  does  not  think  Syllogisms  whenever  he 
speaks  or  writes  Enthymemes.  To  take  another  instance, 
Hamilton's  doctrine  of  the  thoroughgoing  quantification  of 

3* 


58  THE  PRIMARY   AXIOMS   OF   PURE  THOUGHT. 

the  predicate  has  been  objected  to  for  this  reason,  among 
others,  that  the  propositions  which  it  vindicates  are  so  awk- 
ward and  unnatural,  that  they  seem  "  got  up  for  the  purpose 
of  seeing  what  one  can  do."  Perhaps  so ;  and  yet  the 
objection  is  an  idle  one.  For  if  there  ar<5  occasions  when 
we  must  think  affirmative  Judgments  with  universal  predi- 
cates, arid  negative  Judgments  with  particular  ones,  the 
Logician's  first  duty  is  to  express  this  fact,  however  awk- 
ward and  even  ludicrous  such  expression  may  seem 


THE  DOCTRINE   OF   CONCEPTS. 


UNIVERSITY 


CHAPTER   IV. 


THE  DOCTRINE   OF   CONCEPTS. 


I.  Their  Quantity ;  2.  Their  Quality ;   3.  Their  Relation;   4.  Their  Defi- 
nition and  Division. 

A  CONCEPT  is  a  combination,  or  a  reduction  to  unity 
in  Thought,  of  those  elements  and  qualities  of  the 
objects  which  we  are  thinking  of,  whereby  they  are  dis- 
tinguished from  all  other  objects,  and  especially  from  those 
which,  in  other  respects,  are  most  similar  to  them.*  These 
distinguishing  attributes,  which  are  the  elements  of  the 
Concept,  are  called  its  Marks ;  for  through  them  the  ob- 
jects of  Thought  are  determined,  or  known  to  be  what 
they  are,  and  discriminated  from  what  they  are  not.  The 
word,  or  General  Term,  which  is  the  appellation  of  the 
Concept,  is,  consequently,  the  Common  Name  of  all  the 
objects  that  are  included  under  it.  It  is  a  convenient  use 
of  language,  (though  the  words  are  sometimes  applied  in 
a  different  manner,)  to  say  that  the  word  or  Name  connotes 

*  The  words  Concept  and  Notion,  often  used  as  synonymcs,  are  perhaps 
best  distinguished  etymologically ;  —  Concept  (con-capere)  as  the  grasping 
up  together  of  a  plurality  of  attributes  into  one  Thought ;  Notion  (noscert 
nods,  to  know  an  object  by  its  Marks),  as  the  taking  note  of  the  several 
Marks  or  characteristics  of  an  object.  The  meaning  of  Notion  might, 
perhaps,  be  conveniently  limited  to  the  apprehension  of  any  single  Mark 
{nota),  while  Concept  signifies  the  compreliension  of  all  the  attributes  which 
are  characteristic  of  a  certain  class  of  things.  Thus,  I  have  a  Notion  of 
each  of  the  Marks,  cold-blooded,  vertebrated,  animal,  breathing  by  means  of  gills, 
and  living  in  the  water,  taken  singly ;  and  I  have  a  Concept  of  them  taken 
together,  as  the  characteristic  Marks  of  a  Fish,  or  of  the  whole  class  of 
Fishes.     As  thus  limited,  Notions  are  a  subordinate  class  of  Concepts. 


60  THE   DOCTRINE   OF  CONCEPTS. 

the  attributes  or  Marks  which  make  up  its  signification,* 
and  denotes  the  individual  things  contained  under  it  which 
possess  those  attributes.  Thus,  the  name  Man  connotes 
biped,  two-handed,  rational,  animal,  and  denotes  all  indi- 
vidual men  and  classes  of  men. 

It  has  already  been  explained,  that  a  Concept  is  not 
necessarily  the  Thought  of  an  actual,  but  only  of  a  pos- 
sible, class  of  objects ;  that  is,  its  name  may  actually 
denote  only  one  thing,  as,  for  example,  the  one  animal, 
just  discovered,  of  a  species  hitherto  unknown.  Hence, 
Esser  was  led  to  define  a  Concept  as  "  the  representation 
of  an  (one)  object  through  its  distinguishing  Marks."  But 
even  in  this  case,  the  representation,  in  order  to  be  a  Con- 
cept, must  be  a  partial  representation ;  that  is,  it  must 
represent,  not  all  the  Marks,  but  only  the  distinguishing 
Marks.  Thus  it  becomes  the  representative  of  a  possi- 
ble class  or  plurality  of  things  ;  if  other  specimens  should 
be  subsequently  discovered  possessing  these  distinguishing 
Marks,  the  Concept  would  include  them  also.  It  is  only 
when  the  object  is  immediately  presented  before  us  either 
by  the  Senses  or  the  Imagination,  so  that  we  have  a 
Presentation  or  Intuition  of  it,  as  one  whole,  with  all  its 

*  "  As  these  qualities  or  modes  are  only  identified  with  the  thing  by  a 
mental  attribution,  they  are  called  attributes ;  as  it  is  only  in  and  through 
them  that  we  say  or  enounce  aught  of  a  thing,  they  are  called  predicates, 
predicables,  and  predicaments,  or  categories  (these  words  being  here,  used  in 
their  more  extensive  signification);  as  it  is  only  in  and  through  them  that 
we  recognize  a  thing  for  what  it  is,  they  are  called  notes,  signs,  marks,  charac- 
ters ;  finally,  as  it  is  only  in  and  through  them  that  we  become  aware  that 
a  thing  is  possessed  of  a  peculiar  and  determinate  existence,  they  are  called 
properties,  differences,  determinations.  As  consequent  on,  or  resulting  from, 
the  existence  of  a  thing,  they  have  likewise  obtained  the  name  of  consequents. 
"What  in  reality  has  no  qualities  has  no  existence  in  thought,  —  it  is  a 
logical  nonentity ;  hence  e  converso,  the  scholastic  aphorism,  non-entis  njdUx 
sunt  predicata.  What,  again,  has  no  qualities  attributed  to  it,  though  at- 
tributable, is  said  to  be  indetermined ;  it  is  only  a  possible  object  of  thought." 
—  Hamilton,  Lectures  on  logic,  Am.  ed.,  p.  55. 


THEIR  CONTENTS.  63 

attributes,  that  its  Name  is  a  Proper  Name  strictly  so 
called;  for  if  it  is  present  only  in  Thought,  our  repre- 
sentation of  it  is  necessarily  partial,  as  not  including  all  its 
Marks,  and  its  Name  is  then  virtually  Common,  as  the 
designation  of  a  possible  plurality  of  things.  Thus,  if  1 
am  contrasting  in  Thought  two  historical  characters,  as 
Cesar  and  Pompey,  these  two  names  to  my  conception 
become  General  Terms,  as  several  individuals  may  each 
possess  the  few  Marks  which,  for  the  purposes  of  this 
contrast,  I  attribute  to  those  two  old  Romans.  Gray's 
affecting  lines  may  be  attributed  to  any  churchyard :  — 

"  Some  mute  inglorious  Milton  there  may  rest, 

Some  Cromwell,  guiltless  of  his  country's  blood." 

Still  further ;  not  merely  may  a  Concept  actually  denote 
only  one  thing,  it  may  actually  connote  only  one  Mark. 
But  here,  as  before,  there  is  a  possible  plurality  in  actual 
unity.  Thus,  in  the  present  state  of  my  knowledge,  my 
Notion  or  Concept  of  red  color  may  be  absolutely  simple,  — 
that  is,  it  may  have  but  this  one  Mark  of  redness.  But 
additional  acquaintance  with  the  science  of  Optics  would 
teach  me  that  this  red  color  is  an  element  of  white  light, 
and  that  it  has  a  certain  degree  of  refrangibility,  by  virtue 
of  which  its  position  in  the  solar  spectrum  is  at  one  end  of 
the  scale.  Here  are  three  additional  Marks  of  red  color. 
In  like  manner,  every  Concept,  though  actually  simple, 
must  be  regarded  as  containing  a  possible  plurality  of 
Marks.  I  say,  it  must  be  so  regarded ;  for  every  Concept 
must  denote  some  existing  object,  —  existing,  that  is,  either 
really  or  potentially ;  and  no  such  object  can  be  conceived 
of  except  as  possessing  a  possible  plurality  of  Marks. 
For  every  object  can  be  conceived  to  be  what  it  is,  only 
by  discrimmating  it  from  several  things  which  it  is  not; 
and  such  discrimination  is  possible  only  through  a  plurality 
of  attributes. 


02  THE  DOCTRINE  OF  CONCEPTS. 

This  will  be  more  evident,  if  we  consider  for  a  moment 
the  various  kinds  of  Marks  by  which  one  Concept  may 
be  distinguished  from  another.  The  following  enumeration 
of  them,  which  might  be  much  enlarged,  is  taken  in  great 
part  from  Esser. 

Marks  are  divided, — l^Into  affirmative  and  negative,  ac- 
cording as  we  know  through  them  either  what  the  object 
is,  or  what  it  is  not ;  thus,  rational  is  an  Affirmative,  im- 
perfect a  Negative,  Mark  of  Man.  2.  Into  internal  and 
external,  according  as  the  Mark  is  attributed  to  the  object 
either  in  and  for  itself,  or  on  the  ground  of  the  relation 
in  which  it  stands  to  some  other  object ;  thus,  biped  is  an 
Internal,  Father  or  Son  an  External,  Mark  of  Man.  3. 
Into  permanent  and  transitory,  according  as  they  are  al- 
ways, or  only  sometimes,  found  in  the  object ;  thus,  metallic 
is  a  Permanent,  hot  is  a  Transitory,  Mark  of  Iron.  4.  Into 
peculiar  and  common,  according  as  they  belong  to  these 
only,  or  also  to  other  objects ;  thus,  right-angled  is  a  Pe- 
culiar, plane-figure  is  a  Common,  Mark  of  a  Square.  5. 
Into  essential  or  necessary,  and  accidental  or  contingent, 
according  as  they  can,  or  cannot,  be  separated  from  the 
object;  thus,  rational  is  an  Essential,  learned  an  Acci- 
dental, Mark  of  Man.  6.  Into  original  or  immediate,  and 
derivative  or  mediate,  according  as  they  are  either  Marks 
of  the  thing  itself,  or  only  Marks  of  other  Marks  of  it ; 
thus,  free-willed  is  an  Original,  able  to  compute  by  numbers 
a  Derivative,  Mark  of  Man,  the  latter  being  only  a  con- 
sequent or  Mark  of  rationality. 

We  gain  another  view  of  the  elements  of  a  Concept 
by  dividing  them  into,  —  1.  Kinds  of  Existence  ;  2.  Quali- 
ties, or  Modes  of  Existence  ;  and  3.  Relations,  or  Forms 
of  Intermediate  Existence. 

First,  in  order  to  conceive,  we  must  conceive  some- 
thing, —  i.  e.  some  being  or  existence,  —  which,  as  an  object 
of  Thought,  may  be  distinguished  from  other  things,  and 


THEIR   CONTENTS.  68 

to  which  qualities  can  be  attributed.  If  there  is  no  such 
entity,  at  the  bottom  of  the  Concept,  to  give  it  unity,  the 
Thought  is  null;  non-entis  nulla  sunt  predicata.  There 
are  but  two  kinds  of  Being  or  Existence,  one  of  which  is 
thus  necessarily  presupposed  in  Thought;  namely,  Real 
and  Imaginary  or  Potential.  One  or  the  other  must  enter 
into  every  Concept,  not  as  attributed  to  it,  but  as  presup- 
posed in  forming  it.  In  other  words,  every  Thought  must 
be  of  some  real  or  imaginary  thing. 

Secondly,  whatever  exists  must  exist  in  some  deter- 
minate mode  ;  that  is  to  say,  it  must  have  one  or  more 
qualities.  Being  or  existence,  as  defined  above,  includes 
all  things,  both  real  and  possible ;  hence,  in  order  to  think 
any  particular  thing,  we  must  discriminate  it  from  other 
things;  and  we  can  do  this  only  by  attributing  to  it 
Qualities,  or  particular  modes  of  existence.  By  presup- 
posing existence,  then,  we  have  a  thing,  or  object  of  possi- 
ble Thought ;  by  giving  to  it  qualities,  we  have  a  definite 
thing,  or  object  of  actual  Thought.  The  thing  exists  in 
itself,  per  se ;  the  quality  exists  only  in  the  thing,  —  that 
is,  in  something  different  from  itself,  per  aliud,  or,  as  the 
logicians  say,  per  accidens. 

Thirdly,  a  Relation  exists  neither  in  itself,  per  se,  noi 
in  the  thing  as  different  from  itself,  per  aliud,  but  between 
the  thing  and  some  other  thing  with  which  it  is  compared. 
This  intermediate  state  of  existence  is  the  only  character- 
istic feature  of  Relations,  whereby  they  are  distinguished 
from  other  Qualities.  The  Relation  does  not  merely  result 
from  a  comparison  and  discrimination,  for  this  is  true  of 
all  Qualities  ;  but  it  only  exists  as  between  one  thing  and 
another,  thereby  necessitating  a  Thought  of  both.  Thus, 
the  Relation  of  Husband  and  Wife  exists  in  neither  of 
them,  but  between  them,  and  can  be  apprehended  only 
by  thinking  of  the  two  together. 

"  Eveiy  object,"  says  Drobisch,  "  is  thought  as  a  deter- 


64  THE  DOCTRINE  OF  CONCEPTS. 

minate  object  only  through  the  Marks  appertaining  to  it, 
by  means  of  which  it  is  comparable,  in  respect  to  its  nature, 
with  other  things,  and  is  distinguishable  from  them.  With- 
out these  Marks,  it  is  only  an  indeterminate  something,  a 
thing  or  being  without  further  determination ;  just  as,  on 
the  other  hand,  these  Marks  have  no  independent  being  in 
and  for  themselves,  but  they  can  be  separated  only  in 
Thought  from  the  object  in  which  they  exist.  In  the 
Concept  of  the  object,  then,  there  is  the  Thought  of 
an  independent  but  indeterminate  something,  united  with 
determinate,  but  (in  themselves  considered)  dependent, 
Marks ;  the  Concept  of  the  object  is  the  union  of  the  two. 
(Thus,  my  Concept  of  Man  is  a  living,  rational,  organic 
something,  having  a  mortal  body  and  an  immortal  soul.') 
The  Marks  are  the  manifold,  the  plurality,  and  the  in- 
determinate something  is  that  which  gives  unity  to  these 
Marks,  in  the  Concept  of  an  object.  The  Concept  is  com- 
plex, therefore,  and  admits  of  separation  into  its  elements ; 
and  this  separation  is  called  Analysis." 

It  is  obvious  enough,  that  the  distinction  between  Con- 
cept and  Marks  is  not  absolute,  but  relative ;  they  may 
be  used  interchangeably.  Any  Concept  may  become  the 
Mark  of  some  other  Concept;  and  every  Notion,  which 
may  appear  in  one  Thought  as  a  Mark,  becomes  in 
another  an  independent  Concept.  Thus,  the  Concept  ani- 
mal is  a  Mark  of  man;  and  metal,  which  is  a  Mark  of 
iron,  is  itself  a  Concept,  including  under  it  iron,  tin, 
lead,  &c.  The  only  distinction  consists  in  the  two  dif- 
ferent uses  which  are  made  of  them  in  Thought.  If  a 
Concept  is  used  only  as  a  means  of  determining  some 
other  Concept,  and  so  without  direct  reference  to  the  ob- 
jects or  things  which  it  denotes,  it  is  a  Mark ;  but  if  used 
as  a  Class-notion  of  certain  objects,  and  with  only  second- 
ary reference  to  the  attributes  or  qualities  involved  in  it, 
it  is  a  Concept  in  the  stricter  sense.     In  other  words,  if 


THEIR   CONTENTS.  6b 

used  connotatively,  it  is  called  a  Mark;  if  used  denota- 
tively, it  is  called  a  Concept. 

The  only  law  of  pure  Thought  applicable  to  the  forma- 
tion of  Concepts  is  the  Axiom  of  Non-contradiction.  A 
Concept  must  not  have  contradictory  Marks,  as  these  de- 
stroy each  other,  and  the  Thought  so  far  becomes  void  or 
null.  Thus,  looking  only  to  the  Form  of  Thought,  to  the 
Concept  A  may  be  attributed  the  Marks  B,  C,  D,  and  so 
on  without  limitation;  but  B  and  not-B  cannot  be  so 
attributed. 

Looking  to  the  Matter  of  the  Thought,  however,  a 
further  limitation  arises.  Considered  in  relation  to  each 
other,  Marks  are  either  Congruent  or  Repugnant;  the 
former  can,  and  the  latter  cannot,  be  attributed  to  the 
same  Concept.  Thus,  sweet  and  red  are  Congruent,  as  the 
same  apple  may  have  both  Marks ;  but  sweet  and  bitter 
are  Repugnant,  since  they  cannot  be  united  in  the  same 
object;  If  the  tyro  should  object,  that  one  part  of  it  may 
be  sweet,  and  another  part  bitter,  the  answer  is,  that  the 
two  parts  are  two  different  objects.  Marks  are  said  to  be 
Contradictory,  when  the  one  is  a  simple  or  direct  negation 
of  the  other ;  as  sweet  and  not-sweet,  B  and  not-B.  They 
are  Repugnant  or  Contrary,  when  the  negation  is  indirect, 
as  when  the  one  is  denied,  not  directly,  but  by  putting  in 
its  place,  or  in  the  same  Concept,  another  Mark  with  which 
it  is  incompatible.  The  iftere  Form  of  the  Marks  tells 
me  whether  they  are  Contradictory  or  not;  but  to  know 
whether  they  are  Congruent  or  Repugnant,  I  must  know 
the  Matter  of  the  Thought,  —  that  is,  I  must  have  re- 
course to  experience. 

Again,  if  considered  as  mere  Marks,  or  with  reference 
to  their  connotation  only,  the  attributes  which  are  united 
in  the  same  object  are  disparate  Notions,  for  they  are 
different  without  any  similarity.  This  holds  true  of  Con- 
gruent, as  well  as  of  Repugnant,  Marks ;  thus,  sweet  and 


GG  THE  DOCTRINE   OF   CONCEPTS. 

red  are  Disparate,  for  the  quality  of  sweetness  has  no  re- 
semhlance  whatever  with  that  of  redness.  On  the  other 
hand,  if  considered  as  Concepts,  or  with  reference  to  what 
they  denote,  they  are  properly  called  disjunct  or  discrete 
Notions,  for  they  are  only  relatively  different ;  they  have 
at  least  so  much  in  common,  that  they  can  be  co-ordinated 
under  some  higher  Concept.  Thus,  sweet  apples  and  red 
apples  are  so  far  similar,  that  they  both  belong  under  the 
Class-notion  apples  or  fruits.  It  is  only  stating  the  same 
distinction  in  other  words  to  say,  that  Disparate  Notions 
are  Congruent,  for  they  can  be  united  in  the  same  Con- 
cept ;  but  they  do  not  denote  any  objects.  On  the  other 
hand,  the  Disjunct  do  denote  Objects,  but  they  are  not 
Congruent,  for  they  cannot  be  united  in,  but  are  only 
contained  under,  the  same  Concept. 

To  apprehend  still  further  the  nature  of  Concepts,  they 
must  be  viewed  in  three  aspects.  First,  if  considered  in 
themselves  alone,  they  have  Quantity ;  secondly,  if  con- 
sidered in  reference  to  the  mind  or  thinking  subject  in 
which  they  are  conceived,  they  have  Quality ;  thirdly,  if 
considered  in  reference  to  each  other,  they  have  Relation. 

1.   The  Quantity  of  Concepts. 

It  follows  from  the  definition  which  has  been  given, 
that  a  Concept  is  a  magnitude*  or  Quantity,  and  that  this 
Quantity  is  twofold.  First,  it  has  a  number  of  Marks, 
which  are  reduced  to  unity  in  Thought,  because  they  are 
all  conceived  as  inhering  in  one  object  or  thing.  This  is 
its  Quantity  of  Intension.  Secondly,  it  denotes  a  number 
of  objects,  which  are  reduced  to  unity  in  Thought  as  one 
class  or  species,  because  each  of  them  possesses  all  these 
Marks.  This  is  its  Quantity  of  Extension.  Thus,  the 
Intension  of  bird  is  a  winged,  feathered,  vertebrated,  biped, 
animal;  in  its  Extension  are  contained  all  individual  birds 


THEIR   QUANTITY.  67 

and  classes  uf  birds,  as  eagles,  vultures,  hawks,  pigeons,  &c. 
The  plurality  of  objects  which  are  denoted  by  the  Con- 
cept are  said  to  constitute  a  Logical  whole,  or  the  whole 
of  Extension;  the  plurality  of  Marks  connoted  by  the 
Concept  form  a  Metaphysical  whole,  or  the  whole  of 
Intension. 

This  distinction  of  Quantity  has  been  expressed  by  Lo- 
gicians in  various  ways,  which  are  here  enumerated  for 
convenience  of  reference,  though  the  forms  of  expression 
already  given  will  be  adhered  to  in  the  present  work. 

A  Logical  or  Universal  whole  A  Metaphysical  or  Formal  whole  * 

has  Extension,  has  Intension, 
Breadth,  Depth, 

Sphere ;  Comprehension ; 

contains  under  it,  contains  in  it, 

denotes,  connotes, 
Objects,  Marks, 

Things.  Attributes. 

This  twofold  Quantity  of  Concepts  enables  us  to  under- 
stand the  seemingly  opposite  assertions,  that  the  Subject 
of  a  proposition  is  in  the  Predicate,  and  yet  that  the  Predi- 
cate is  in  the  Subject.     With  reference  to  the  Quantity 

*  Besides  the  Logical  and  the  Metaphysical,  three  other  sorts  of  wholes 
have  been  distinguished  by  Logicians. 

1.  The  Essential  or  Physical  whole  is  that  which  consists  of  Matter  and 
Form,  or  substance  and  accident,  as  its  essential  parts.  The  characteristic 
of  this  whole  is,  that,  as  its  parts  do  not  exist  out  of  each  other,  they  cannot 
be  separated  except  in  Thought.  As  Burgersdyck  says,  "the  Form  per- 
meates the  Matter,  and  informs  all  its  parts,"  so  that  Form  and  Matter  are 
inseparable. 

2.  The  Mathematical  or  Integral  whole,  on  the  other  hand,  has  parts 
which  are  external  to  each  other,  so  that  they  can  be  divided  asunder. 
This  is  the  case  with  geometrical  figures,  as  the  triangle,  the  parallelogram, 
and  with  the  human  body  and  the  limbs.     These  have  partes  extra  partes. 

3.  A  Collective  whole,  or  whole  of  Aggregation,  has  its  parts  separate 
and  accidentally  thrown  together ;  as,  an  army,  a  heap  of  stones. 


08  THE   DOCTRINE   OF   CONCEPTS. 

of  Intension,  the  Predicate  is  in  the  Subject,  inasmuch 
as  it  is  but  one  of  several  Marks  which  make  up  our 
Notion  of  the  Subject.  Thus,  man  is  animal;  animal  may 
be  regarded  as  a  part  of  man,  because  it  is  a  part  of  the 
meaning  of  the  word ;  and,  when  taken  in  connection  with 
the  other  parts,  living,  two-handed,  rational,  makes  up  the 
whole  Intension  of  the  Concept  man.  But  in  respect  to 
the  Quantity  of  Extension,  man  is  contained  under  an- 
imal, —  the  Subject  in  the  Predicate,  —  since  he  is  but  one 
out  of  many  kinds,  all  denoted  by  this  one  General  Term, 
or  contained  under  this  one  Concept,  animal. 

"  We  find  two  expressions  in  Aristotle,  both  of  which 
are  sometimes  rendered  by  '  being  in,''  —  inesse.  1.  vnapxeiv, 
by  which  the  Predicate  is  said  to  be  in  the  Subject.     This 

is  equivalent  to  KaTrjyopelcrOai.  To  A  vnapxa  navrl  t<3  B  =  to 
A   KaTTjyopdTai   Kara  navros  rov   B  =  A   inest   Omni   B    (=  A    is 

predicated  of  every  B  =  All  B  is  A).  2.  tlvai  iv,  by  which 
the  Subject  is  said  to  be  in  the  Predicate.  A  ianp  iv  oXo> 
r<a  B  =  Omne  A  est  B  QAll  A  is  B).  This  is  exactly  the 
reverse  of  Karrfyoptirau  The  English  language  is  defective 
in  not  having,  like  the  Greek  and  Latin,  a  proper  Copula 
to  express  the  relation  of  Intension  as  well  as  that  of  Ex- 
tension. Thus  the  relation  expreesed  by  V7r«px«  and  inest 
can  only  be  strictly  rendered  into  English  by  a  circum- 
locution, '  A  is  a  quality  belonging  to  B.'  With  the  ordi- 
nary Copula,  both  must  be  translated  into  the  language  of 
Extension."  * 

Besides  the  Concepts  which  are  formed  from  individual 
things,  by  abstracting  their  differences  and  uniting  their 
common  or  similar  elements,  we  can,  by  a  perfectly  similar 
process,  form  Concepts  of  Concepts ;  and  then,  again  re- 
peating this  process,  we  obtain  Concepts  of  these  Concepts, 
and  so  on  indefinitely.     In  this  way,  we  have  in  each  case 

*  Mansel,  Notes  to  Aldrick,  p.  45. 


THEIR    QUANTITY.  £)9 

a  hierarchy  of  Concepts,  of  which  only  the  lowest  m  order 
directly  denotes  individuals,  while  all  the  others  directly 
denote  other  Concepts  or  classes,  and  only  indirectly  denote 
the  individuals  contained  in  those  classes.  Thus,  spaniel, 
terrier,  hound,  mastiff,  &c.  are  Concepts  of  the  first  or 
lowest  order,  each  of  them  directly  denoting  certain  indi- 
vidual animals,  whose  common  attributes  have  become,  in 
Thought,  the  Marks  of  their  class.  Then,  abstracting  the 
differences  of  these  classes,  we  have  dog  as  a  Concept  of 
the  second  order,  directly  denoting  spaniel,  terrier,  &c,  and 
indirectly  denoting  the  same  individuals  as  before.  Having 
formed  in  a  similar  manner  secondary  Concepts  of  eat,  wolf, 
fox,  bear,  &c,  by  comparing  all  of  these  with  dog,  abstracting 
the  differences  and  combining  the  similarities,  we  obtain  the 
tertiary  Concept  carnivora.  Again,  comparing  carnivora 
with  rodents,  marsupials,  ruminants,  &c,  we  have  a  Con- 
cept of  the  next  higher  order,  mammal,  of  which  the  Marks, 
forming  the  Intension,  are  vertebrate,  viviparous,  warm-blood- 
ed, animal,  suckling  its  young.  It  is  evident  that  we  can 
go  on  in  this  manner,  rising  through  Concepts  successively 
broader  and  broader  in  generalization,  till  we  reach  the 
limit  of  human  Thought  in  the  Concept  thing,  entity,  or 
object  of  Thought,  which  connotes  nothing  but  existence 
(real  or  potential),  and  denotes  everything. 

I  have  here  intentionally  taken  an  illustration  of  the  log- 
ical process  of  generalization  from  Natural  History,  as  the 
science  in  which  classification  is  most  extensive  and  precise, 
though  with  the  disadvantage  of  introducing  here  a  number 
of  technical  names  peculiar  to  that  science,  and  with  which, 
as  belonging  to  the  Matter  of  Thought,  Logic  has  nothing 
to  do.  But  every  word  in  our  language,  or  in  any  language, 
perfectly  corresponds  to  one  of  these  zoological  technicali- 
ties, in  that  it  occupies  a  definite  place  in  some  one  of  the 
countless  hierarchies  of  Concepts  which  the  human  mind, 
for  various  purposes,  has  been  led  to  form.     The  greater 


7Q  THE  DOCTRINE  OF  CONCEPTS. 

part  of  our  mental  life  is  spent  in  generalizing  by  successive 
steps,  —  that  is,  in  forming  Concepts  of  Concepts ;  —  but 
always,  except  in  the  science  of  Logic,  with  special  refer- 
ence to  the  particular  things  denoted  by  these  Concepts. 
Logic,  which  deals  only  with  the  Form,  and  not  the  Matter, 
of  Thought,  needs  a  set  of  technicalities  of  its  own,  to  de- 
scribe these  steps  of  generalization,  and  all  other  processes 
of  pure  Thought,  with  reference,  not  to  the  things  which 
they  denote,  but  to  each  other  and  to  the  thinking  mind. 
This  is  precisely  the  distinction,  so  famous  in  the  Scholastic 
philosophy,  between  first  and  second  intentions,  —  a  distinc- 
tion which  has  been  ignorantly  ridiculed  by  those  who  did 
not  understand  it,  but  which  in  itself  is  perfectly  intelligible, 
and  is  as  necessaiy  as  other  technical  distinctions  in  science, 
all  of  which,  before  they  can  be  understood,  require  a 
knowledge  of  the  elements  of  the  special  science  in  which 
they  are  taken.  The  burlesque  question,  utrum  chimcera 
bombinans  in  vacuo  posset  comedere  secundas  intentiones,  is  a 
good  specimen  of  the  fun  which  for  a  long  time  was  heaped 
on  the  study  of  Scholastic  Logic. 

A  first  intention  or  notion  is  a  Concept,  whether  of  a  low 
or  a  high  order,  which  denotes  things.  Thus,  in  the  illus- 
tration just  given,  spaniel,  dog,  carnivor,  mammal,  —  each 
and  all  denote  certain  animals ;  they  are  First  Intentions. 
On  the  other  hand,  a  second  intention  or  notion  is  a  Concept 
which  denotes  first  intentions  —  i.  e.  the  former  Concepts  — 
in  their  relation,  not  to  the  things  denoted,  but  to  each  other. 
Thus,  if  the  three  lower  steps  in  every  hierarchy  of  Con- 
cepts are  denominated  respectively,  Variety,  Species,  Genus, 
then  these  three  names,  applicable  not  only  to  spaniel,  dog, 
carnivor,  but  to  every  other  corresponding  set  of  three  suc- 
cessive steps  of  generalization,  express  second  intentions, 
44  First  Intentions,"  says  Mr.  Mansel,  44  as  conceptions  of 
things,  are  predicable  of  the  individuals  conceived  under 
them.     Thus  we  may  say,  4  Socrates  is  man,  animal,  &c.' 


THEIR   QUANTITY.  71 

Second  Intentions  are  not  so  predicable;  we  cannot  say, 
4  Socrates  is  species,  genus,  &c.'  So,  when  Genus  is  said  to 
be  predicable  of  Species,  it  is  not  meant  that  we  can  predi- 
cate the  one  Second  Intention  of  the  other,  so  as  to  say, 
4  Species  is  Genus ' ;  but  that  the  First  Intention  animal 
is  predicable  of  the  First  Intention  man,  the  relation  of  the 
one  to  the  other  being  expressed  by  the  Second  Intentions 
genus  and  species.  For  this  reason,  Logic  was  said  to  treat 
of  second  intentions  applied  to  first."  * 

It  is  obvious  that  Second  Intentions  are  the  peculiar  tech- 
nicalities of  the  abstract  sciences  of  Logic  and  Grammar. 
In  the  physical  sciences,  we  have  to  deal  only  with  Con- 
cepts of  things ;  but  Logic  and  Grammar  need  Concepts 
of  our  modes  of  thinking  and  speaking  of  things,  so  far  as 
these  modes  are  related  to  each  other.  Thus,  we  need  the 
technical  terms  Genus  and  Species  to  express  the  relations 
in  which  the  several  Concepts,  that  form  any  one  hierarchy 
or  series,  stand  to  each  other.  These  relations  are  indicat- 
ed in  the  following  table. 

•  Notes  to  Aldrich,  p.  20. 


72 


THE  DOCTRINE  OF  CONCEPTS. 


Second  Intentions, 
or  Concepts  of  Con- 
cepts, as  thought  rel- 
atively to  each  other. 


Summum  Genus. 

Species  or  subal- 
tern Genus. 


Species  or  subal- 
tern Genus. 


Species  or  subal- 
tern Genus. 


Species  or  subal- 
tern Genus. 


Infima  Species. 


First  Intentions, 

or  Concepts  of 

tilings. 


Thing  or  Entity. 
Animal. 


Mammal. 


Carnivor. 


Dog. 


Spaniel. 


Intension, 
or  Marks  cou noted. 


Existing. 

Existing,  organized, 
sentient. 


Existing,  organized, 
sentient,  suckling 
their  young. 

Existing,  organized, 
sentient,  suckling 
their  young,  eat- 
ing flesh. 

Existing,  organized, 
sentient,  suckling 
their  young,  eat- 
ing flesh,  digiti- 
grade  quadruped, 
&c. 

Silky-haired,  water- 
dog,  having  all  the 
preceding  Marks. 


Extension, 
or  Objects  denoted. 


Everything. 

Every  Vertebrate, 
Mollusk,  Artic- 
ulate, and  Ra- 
diate. 

Every  vertebrat- 
ed  animal  which 
suckles  its  young. 

Bears,  wolves, 
foxes,  lions, 
tigers,    &c. 


Mastiffs,  spaniels, 
hounds,  terri- 
ers, &c. 


All      individual 
spaniels. 


Put  any  other,  an  entirely  different,  series  of  First  In- 
tentions in  the  place  of  those  given  in  the  table,  —  take, 
for  instance,  the  series  Man,  European,  Frenchman,  Paris- 
ian,  —  and  it  is  evident  that  the  relations  of  these  Con- 
cepts also  to  each  other  will  be  correctly  indicated  by  the 
same  Second  Intentions  as  before.  Man  is  now  the  Sum- 
mum  Genus,  Parisian  is  the  Infima  Species,  and  the  inter- 
mediate Concepts  are  the  Subaltern  Genera  or  Species. 

A  mere  inspection  of  the  table  also  brings  to  light  the 
one  law  of  Thought  which  determines  the  Quantity  of 
Concepts.  It  is,  that  Intension  and  Extension,  the  two 
Quantities  of  every  Concept,  are  always  in  inverse  ratio  to 
each  other.     They  must  both  be  present ;  there  must  be  at 


THEIR   QUANTITY.  73 

least  a  minimum  of  each ;  for  a  Concept  muse  always  con- 
note something  and  always  denote  something.  But  if  we 
take  a  great  number  of  objects,  we  can  find  but  few  attri- 
butes or  Marks  which  are  common  to  them  all,  while  a  few 
objects  may  have  many  common  attributes.  Looking  at 
the  table,  we  see  that,  in  the  Summum  Genus,  the  Inten- 
sion is  least:  in  the  case  there  given,  only  one  Mark  — 
existing  —  is  connoted ;  while  the  Extension  is  greatest,  for 
the  same  Concept  denotes  everything.  Descending  from 
the  Highest  Genus,  we  see  that  the  Intension  steadily  in- 
creases through  the  Subaltern  Genera,  while  the  Extension 
regularly  diminishes.  In  the  Lowest  Species,  the  Intension 
is  at  its  maximum,  as  Spaniel  connotes  all  the  Marks  of  the 
higher  Genera  and  one  or  two  additional  Marks,  and  the 
Extension  is  at  its  minimum,  as  there  are  fewer  Spaniels 
than  Dogs,  still  fewer  than  Carnivora,  &c.  It  is  only  stat- 
ing the  same  law  in  other  words  to  say,  with  reference  to 
any  one  hierarchy  or  series  of  Concepts,  that  any  increase 
of  the  Intension  produces,  ipso  facto,  a  diminution  of  the 
Extension,  and  any  diminution  of  the  former  an  increase 
of  the  latter.  Observe,  however,  that  it  is  only  the  origi- 
nal and  essential  Marks  of  which  we  speak,  when  we  say 
that  the  number  of  Marks  is  inversely  proportional  to  the 
number  of  objects  denoted.  The  Original  Marks  carry 
their  Derivatives  along  with  them  by  necessary  implica- 
tion ;  and  therefore  we  do  not  really  increase  the  Intension, 
but  only  render  it  more  explicit,  when  we  annex  certain 
Derivative  attributes  which  were  not  formerly  expressed  — 
perhaps  not  even  thought  —  as  belonging  to  it.  Thus,  the 
Intension  of  triangle,  as  a  plane  figure  having  only  three 
sides  and  three  angles,  is  not  at  all  enlarged  by  adding  this 
Mark,  the  sum  of  these  three  angles  being  equal  to  two  right 
angles,  even  though  I  now  for  the  first  time  learn  that  this 
is  their  sum.  Though  I  did  not,  therefore,  previously  think 
this  Mark  of  the  Concept,  it  did  nevertheless  belong  to  it 


74  THE  DOCTRINE  OF  CONCEPTS. 

implicitly,  or  by  necessary  inference  ;  and  hence  its  express 
recognition  does  not  alter  either  Quantity.  In  like  man- 
ner, it  is  only  the  Essential  Marks  which  determine  the 
boundaries  of  a  Concept ;  we  do  not  enlarge  the  Intension 
of  man  as  a  rational  animal,  by  adding  this  Accidental 
Mark,  sometimes  learned.  As  for  the  Mark  capable  of 
learning,  that  is  a  Derivative  from  rational. 

The  metaphysical  meaning  of  essence  is,  that  internal 
constitution  of  a  thing  which  makes  it  what  it  is,  —  which  is 
not  only  the  source  of  its  attributes,  but  is  necessary  to  its 
existence.  In  this  sense,  of  course,  no  finite  mind  can 
attain  to  a  knowledge  of  the  Essence  of  any  real  thing 
whatever.  Passing  by  the  disputes  on  this  head  as  be- 
yond our  province,  it  is  enough  to  say  that  Logic  (which 
has  nothing  to  do  with  "  real  things,"  as  they  belong  to 
the  Matter  of  Thought)  considers  the  Essence  of  a  Con- 
cept to  be  the  aggregate  of  its  Marks,  or,  in  other  words, 
the  sum  of  the  attributes  which  it  connotes.  Still  further:  — 
Formal  Logic  cannot  inquire  into  the  nature  of  these  at- 
tributes, but  designates  them  indifferently  by  letters  of 
the  alphabet,  as  being  all  of  the  same  kind.  It  necessarily 
presupposes,  as  above  stated,  that  only  Original  and  Es- 
sential attributes  are  used  as  Marks  of  a  Concept;  and 
hence  it  looks  only  to  their  number,  and  not  to  their 
quality.  Therefore,  the  law  is  universal  and  absolute, — 
add  or  subtract  a  single  Mark,  and  the  Extension,  or 
number  of  objects  denoted,  is  thereby  diminished  or  in- 
creased. Essential  means  inseparable  or  necessary ;  take 
away  an  Essential  attribute,  and  the  Concept  ceases  to  be 
what  it  was,  and  becomes  another  Concept  with  a  wider 
Extension.  Thus,  from  man  as  a  rational  animal,  remove 
the  Mark  of  rationality,  which  is  Essential  to  him,  and 
the  remaining  Concept  is  animal,  which  denotes  all  men 
and  brutes  also. 

Generification,  usually  called  Generalization,  is  the  pro- 


THEIR   QUANTITY.  75 

cess  of  rising,  through  the  successive  abstraction  of  Marks, 
from  lower  to  higher  Concepts.  It  is  so  called  because  the 
lower  Concept  is  relatively  a  Species,  and  the  higher  one, 
to  which  we  proceed,  is  relatively  a  Genus,  having  a  wider 
Extension.  Thus,  we  proceed  from  the  lower  Concept 
Mammal,  which  is  in  this  relation  a  Species,  to  the  higher 
Concept  Animal,  which  is  in  the  same  relation  a  Genus, 
by  throwing  out  the  Mark  suckling  their  young.  The 
name  of  this  process,  therefore,  correctly  indicates  the  act 
of  becoming  a  Genus. 

The  contrary  process,  of  descending  from  higher  to  low- 
er Concepts  through  the  successive  assumption  of  Marks, 
is  called  Determination,  —  more  properly  Specification,  as 
it  expresses  the  act  of  becoming  a  Species.  It  has  been 
well  said,  that  it  is  the  process  of  "  thinking  out  objects 
by  thinking  in  attributes."  Thus,  we  descend  from  the 
Genus  Mammalia  to  the  Species  Carnivora,  by  throwing 
out  all  herbivorous  animals,  through  bringing  in  the  Mark, 
eating  flesh. 

It  has  already  been  observed,  in  treating  of  the  Axiom 
of  Excluded  Middle  and  its  applications,  that  every  pair 
of  Contradictory  attributes,  A  and  not-A,  divide  the  uni- 
verse between  them,  as  one  or  the  other  must  belong  to 
everything.  Because  a  given  attribute,  A,  can  be  affirmed 
only  of  a  certain  number  of  objects,  it  must  be  denied  of 
all  other  objects;  and  we  may  express  such  denial  by 
saying,  all  these  others  are  Not-A.  Hence  we  have  a 
peculiar  class  of  Concepts,  called  Negative  or  Privative, 
more  properly  Infinitated,  of  which  the  characteristic  is, 
that  they  denote  almost  everything,  and  connote  « next  to 
nothing,'  —  that  is,  nothing  positive.  Thus  they  afford  a 
curious  illustration  of  the  law,  that  the  two  quantities  of  a 
Concept  exist  only  in  an  inverse  proportion  to  each  other. 
Logically  considered,  the  Extension  of  the  Concept  Not-A 
is  infinite,  embracing  the  universe  of  existence  both  real 


76  THE  DOCTRINE  OF  CONCEPTS. 

and  potential ;  for  the  subtraction  of  a  finite  quantity,  .A, 
does  not  diminish  infinity.  Consequently,  its  Intension  is 
zero ;  for  it  does  not  connote  any  Mark,  but  only  the 
absence  of  the  Mark,  A. 

Practically  considered,  however,  or  with  reference  to 
the  Matter  of  the  Thought,  "  the  universe  "  in  such  cases 
is  not  thought  absolutely,  but  relatively ;  it  means  only 
the  totality  of  that  class  of  objects  which  we  are  thinking 
of,  and  to  which  A  belongs.  Thus,  the  two  Concepts 
Frenchman  and  not-Frenchman  are  not  thought  to  include 
all  things,  (which,  if  taken  strictly,  they  would  do,)  but 
only  all  men.  In  like  manner,  not-male,  which,  if  rigidly 
construed,  would  denote  every  stock  and  stone,  besides 
many  animals,  is  actually  thought  merely  as  a  synonyme 
for  female,  and  so  denotes  only  about  one  half  of  the  ani- 
mal kingdom.  Sometimes,  the  name  is  seemingly  positive, 
but  the  Concept  or  thought  is  truly  negative.  Thus, 
parallels  are  lines  that  do  not  meet ;  therefore,  as  two 
negatives  destroy  each  other,  not-parallel  are  lines  that  do 
meet,  —  a  really  positive  Concept  under  a  Privative  or 
Infinitated  form.  For  this  reason,  some  writers  have  ar- 
gued that  infinite,  i.  e.  not-finite,  is  not  thought  negatively, 
but  positively ;  for  finite,  meaning  limited  or  bounded,  is  a 
restriction  or  negation  of  the  magnitude  which  infinity 
asserts  positively.  On  the  other  hand,  it  is  maintained 
that  the  essence  of  Thought,  as  such,  consists  in  limitation 
or  restriction  ;  for  we  cannot  think  any  object  except  by 
distinguishing  it,  through  its  peculiar  Marks,  from  other 
objects  ;  consequently,  to  deny  this  restriction  or  negation, 
is  to  deny  that  the  object  in  question  has  any  peculiar 
Marks,  or  that  it  is  distinguished  from  other  objects  in  any 
manner  whatever,  and  thereby  to  reduce  the  Thought  of 
it  to  zero. 


THEIR   QUALITY.  '<  7 


2.     The  Quality  of  Concepts. 

When  considered  in  relation  to  the  mind  or  thinking 
subject  in  which  they  are  conceived,  Concepts  may  be 
said  to  have  Quality,  according  as  they  more  or  less 
perfectly  represent  to  this  mind  the  objects  which  they 
denote,  and  .the  Marks  or  attributes  by  which  those  objects 
are  distinguished.  The  three  virtues  of  Clearness,  Distinct- 
ness, and  Adequacy  constitute  the  perfection  of  Thought. 
The  corresponding  vices,  of  course,  which  render  Thought 
imperfect,  are  Obscurity,  Indistinctness,  and  Inadequacy. 
The  Quality  of  a  Concept  depends  on  the  degree  in  which 
it  possesses  each  of  these  merits  or  faults. 

It  is  evident,  from  this  account,  that  the  Quality  of 
Concepts,  depending  on  the  characteristics  not  merely  of 
possible,  but  of  perfect,  Thought,  properly  belongs  either 
to  the  Doctrine  of  Method,  or  to  what  Hamilton  calls 
Modified  Logic,  rather  than  to  Pure  Universal  Logic.  As 
the  subsidiary  processes  of  Definition  and  Division,  however, 
by  which  the  Qualities  of  Clearness,  Distinctness,  and  Ad- 
equacy are  obtained,  are  applicable  to  all  Concepts,  and, 
in  a  certain  degree,  regulate  their  formation  and  use  in  all 
minds,  there  is  sufficient  reason  for  considering  the  subject 
here,  instead  of  regarding  it  as  a  mere  appendage  to  the 
science,  to  be  treated  only  at  the  close.  It  is  sometimes 
convenient  to  depart  a  little  from  a  rigorously  systematic 
arrangement,  more  being  gained  than  lost  by  the  sacrifice. 
For  this  reason,  and  even  as  a  matter  of  necessity,  several 
matters  properly  appertaining  to  the  Relation  of  Concepts 
have  been  partially  considered  in  the  preceding  section, 
under  the  head  of  their  Quantity.  The  filiation  and  inter- 
dependence of  the  parts  of  a  science  are  often  such,  that 
it  is  impossible  to  give  a  proper  explanation  of  any  one 
of  them  without  presupposing  some  knowledge  of  the 
others. 


78  THE  DOCTRINE   OF   CONCEPTS. 

A  Concept,  being  the  reduction  of  a  plurality  both  of 
Marks  and  Objects  to  unity,  supposes  the  power  of  thinking 
one  and  many  both  separately,  and  in  their  relation  to  each 
other,  or  together.  We  think  the  Concept  clearly  as  a 
unity,  when  we  can  clearly  distinguish  it  as  one  whole 
from  other  unities,  —  that  is,  from  other  Concepts  regarded 
as  wholes.  We  think  it  distinctly  as  a  plurality,  when 
we  can  distinguish  both  the  Marks  and  the  Objects  which 
constitute  it  from  each  other.  The  Clearness  of  my 
Concept  of  a  given  metal  —  iron,  for  instance  —  depends 
on  the  fulness  and  precision  with  which  I  distinguish  it 
as  one  whole  from  other  Concepts,  especially  of  those 
substances  which,  like  the  other  metals,  tin,  copper,  plati- 
num, as  nearest  or  most  similar,  would  be  most  likely  to 
be  confounded  with  it.  The  opposite  of  this  merit  is  Ob- 
scurity. On  the  other  hand,  the  Distinctness  of  a  Concept 
depends  on  the  fulness  and  precision  whereby  I  apprehend 
it  as  a  plurality,  —  that  is,  as  connoting  many  attributes 
or  Marks,  which  I  clearly  distinguish  from  each  other, 
and  as  denoting  many  Objects,  which  also  I  can  clearly 
distinguish  from  each  other.  The  former,  or  the  dis- 
tinct apprehension  of  the  several  Marks,  is  its  Internal 
Distinctness;  the  latter,  the  distinct  apprehension  of  the 
several  Objects  contained  under  it,  is  its  External  Dis- 
tinctness.    The  opposite  of  this  merit  is  Indistinctness. 

It  is  evident  that  these  qualities  of  a  perfect  Concept 
may  exist  in  an  indefinite  number  of  degrees ;  and  it  is 
also  evident,  that  a  Concept  may  be  quite  Clear,  while 
it  is  but  very  imperfectly  Distinct.  A  young  child  may 
have  a  very  Clear  notion  of  a  clock,  as  distinguished  from 
the  other  objects  in  the  room,  and  still  have  but  a  very 
Indistinct  apprehension  of  its  parts,  properties,  and  uses, 
or  of  the  various  kinds  of  horological  instruments  all 
denoted  by  this  name.  On  the  other  hand,  Distinctness 
necessarily  involves  Clearness  ;  I  cannot  have  a  Distinct 


THEIR   QUALITY.  79 

apprehension  of  all  the  Marks  of  a  Concept,  without  being 
thereby  enabled  clearly  to  distinguish  it  as  one  whole  from 
other  Concepts.  The  fact,  that  we  may  be  able  very 
clearly  to  discriminate  a  whole  from  other  wholes,  or  a 
Concept  from  other  Concepts,  though  we  can  but  indis- 
tinctly separate  in  thought  the  parts  or  the  Marks  which 
constitute  that  whole  or  that  Concept,  is  thus  illustrated 
by  Hamilton,  from  the  analogy  of  our  Perceptive  and 
Representative  Faculties. 

"  We  are  all  acquainted  with  many,  say  a  thousand,  indi- 
viduals ;  that  is,  we  recognize  such  and  such  a  countenance 
as  the  countenance  of  John,  and  as  not  the  countenance  of 
James,  Thomas,  Richard,  or  any  of  the  other  999.  This 
we  do  with  a  clear  and  certain  knowledge.  But  the  coun- 
tenances which  we  thus  distinguish  from  each  other  are, 
each  of  them,  a  complement  made  up  of  a  great  number 
of  separate  traits  or  features ;  and  it  might,  at  first  view, 
be  supposed  that,  as  a  whole  is  only  the  sum  of  its  parts, 
a  clear  cognition  of  a  whole  countenance  can  only  be  re- 
alized through  a  distinct  knowledge  of  each  of  its  constitu- 
ent features.  But  the  slightest  consideration  will  prove 
that  this  is  not  the  case.  For  how  few  of  us  are  able  to 
say  of  any,  the  most  familiar  face,  what  are  the  particular 
traits  which  go  to  form  the  general  result:  and  yet,  on 
that  account,  we  hesitate  neither  in  regard  to  our  own 
knowledge  of  an  individual,  nor  in  regard  to  the  knowl- 
edge possessed  by  others.  Suppose  a  witness  be  adduced 
in  a  court  of  justice  to  prove  the  identity  or  non-identity 
of  a  certain  individual  with  the  perpetrator  of  a  certain 
crime,  the  commission  of  which  he  had  chanced  to  see ;  — 
would  the  counsel  be  allowed  to  invalidate  the  credibility 
of  the  witness  by,  first  of  all,  requiring  him  to  specify  the 
various  elements  of  which  the  total  likeness  of  the  accused 
was  compounded,  and  then  by  showing  that,  as  the  witness 
either  could  not   specify  the  several   traits,  or  specified 


80  THE  DOCTRINE  OF  CONCEPTS. 

what  did  not  agree  with  the  features  of  the  accused,  he 
was  therefore  incompetent  to  prove  the  identity  or  non- 
identity  required  ?  This  would  not  be  allowed.  For  the 
court  would  hold  that  a  man  might  have  a  clear  perception 
and  a  clear  representation  of  a  face  and  figure,  of  which, 
however,  he  had  not  separately  considered,  and  could  not 
separately  image  to  himself,  the  constituent  elements. 
Thus,  even  the  judicial  determination  of  life  and  death 
supposes,  as  real,  the  difference  between  a  clear  and  a 
distinct  knowledge :  for  a  distinct  knowledge  lies  in  the 
knowledge  of  the  constituent  parts ;  while  a  clear  knowl- 
edge is  only  of  the  constituted  whole. 

u  Continuing  our  illustrations  from  the  human  counte- 
nance ;  we  all  have  a  clear  knowledge  of  any  face  which 
we  have  seen,  but  few  of  us  have  distinct  knowledge  even 
of  those  with  which  we  are  familiar ;  but  the  painter,  who, 
having  looked  upon  a  countenance,  can  retire  and  repro- 
duce its  likeness  in  detail,  has  necessarily  both  a  clear  and 
a  distinct  knowledge  of  it.  Now,  what  is  thus  the  case 
with  perceptions  and  representations,  is  equally  the  case 
with  notions.  We  may  be  able  clearly  to  discriminate  one 
concept  from  another,  although  the  degree  of  consciousness 
does  not  enable  us  distinctly  to  discriminate  the  various 
component  characters  of  either  concept  from  each  other." 

Clearness  and  Distinctness,  with  their  opposites,  were 
first  regarded  as  qualities  of  vision  merely,  being  applied 
only  to  objects  as  seen,  their  signification  being  afterwards 
extended  by  analogy  to  the  other  senses,  and  finally  to 
Thought.  The  distinction  between  them,  first  fully  pointed 
out  by  Leibnitz,  was  admirably  illustrated  by  Krug,  in  a 
passage  which  is  thus  paraphrased  by  Hamilton. 

"In  darkness  —  the  complete  obscurity  of  night- — we 
see  nothing,  —  there  is  no  perception,  —  no  discrimination 
of  objects.  As  the  light  dawns,  the  obscurity  diminishes, 
the  deep  and  uniform  sensation  of  darkness  is  modified, — 


THEIB   QUALITY.  81 

we  are  conscious  of  a  change,  —  we  see  something,  but 
are  still  unable  to  distinguish  its  features, — we  know  not 
what  it  is.  As  the  light  increases,  the  outlines  of  wholes 
begin  to  appear,  but  still  not  with  a  distinctness  sufficient 
to  allow  us  to  perceive  them  completely;  but  when  this 
is  rendered  possible,  by  the  rising  intensity  of  the  light, 
we  are  then  said  to  see  clearly.  We  then  recognize 
mountains,  plains,  houses,  trees,  animals,  etc.,  that  is,  we 
discriminate  these  objects  as  wholes,  as  unities,  from  each 
other.  But  their  parts,  —  the  manifold  of  which  these 
unities  are  the  sum,  —  their  parts  still  lose  themselves  in 
each  other;  they  are  still  but  indistinctly  visible.  At 
length,  when  the  daylight  has  fully  sprung,  we  are  en- 
abled likewise  to  discriminate  their  parts;  we  now  see 
distinctly  what  lies  around  us.  But  still  we  see  as  yet 
only  the  wholes  which  lie  proximately  around  us,  and  of 
these,  only  the  parts  which  possess  a  certain  size.  The 
more  distant  wholes,  and  the  smaller  parts  of  nearer 
wholes,  are  still  seen  by  us  only  in  their  conjoint  result, 
only  as  they  concur  in  making  up  that  whole  which  is  for 
us  a  visible  minimum.  Thus  it  is,  that  in  the  distant  for- 
est, or  on  the  distant  hill,  we  perceive  a  green  surface ; 
but  we  see  not  the  several  leaves,  which  in  the  one,  nor 
the  several  blades  of  grass,  which  in  the  other,  each  con- 
tributes its  effect  to  produce  that  amount  of  impression 

which  our  consciousness  requires Clearness  and 

distinctness  are  thus  only  relative.  For  between  the  ex- 
treme of  obscurity  and  the  extreme  of  distinctness  there 
are  in  vision  an  infinity  of  intermediate  degrees.  Now, 
the  same  thing  occurs  in  thought.  For  we  may  either  be 
conscious  only  of  the  concept  in  general,  or  we  may  also 
be  conscious  of  its  various  constituent  attributes,  or  both 
the  concept  and  its  parts  may  be  lost  in  themselves  to  con- 
sciousness, and  only  recognized  to  exist  by  effects  which 
indirectly  evidence  their  existence." 


82  THE  DOCTRINE   OF   CONCEPTS. 

The  Adequacy  of  a  Concept  depends  on  the  number 
and  the  relative  importance  of  the  Marks  which  constitute 
it,  considered  as  more  or  less  perfectly  representing  the 
objects  which  it  denotes.  A  Concept  may  be  perfectly 
Clear  and  perfectly  Distinct,  and  still  be  a  very  Inadequate 
representation  of  the  class  of  things  for  which  it  stands ; 
for  it  may  connote  but  two  or  three  out  of  the  many 
attributes  which  they  possess,  and  even  these  two  or  three 
may  be  relatively  insignificant,  or  of  trifling  import  as  com- 
pared with  several  of  those  which  are  omitted.  The  old 
Concept  of  man,  happily  ridiculed  by  Aristotle,  which 
described  him  as  a  two-legged  animal  without  feathers,  is 
Clear,  for  it  enables  us  easily  to  distinguish  man  from  all 
other  animals ;  and  it  is  Distinct,  for  its  three  Marks  are 
easily  distinguishable  from  each  other ;  but  it  is  very 
[nadequate,  as  it  omits  man's  crowning  and  peculiar  at- 
tribute as  a  rational  being.  We  may  have  a  very  Clear 
and  Distinct  Concept  of  an  elephant,  as  a  quadruped  that 
drinks  through  its  nostrils;  obviously,  however,  this  is  a 
rery  Inadequate  representation  of  that  sagacious  and  gi- 
gantic brute. 

The  difference  between  the  artificial  system  of  Botany 
invented  by  Linnaeus  and  the  Natural  System  of  Jussieu 
illustrates  very  well  the  importance  of  making  a  proper 
selection,  and  taking  a  sufficient  number,  of  attributes 
wherewith  to  determine  the  classes  of  things  which  we 
think.  Every  plant  may  be  perfectly  distinguished  from 
all  other  plants,  and  easily  referred  to  its  proper  class,  in 
a  system  founded,  like  that  of  Linnaeus,  exclusively  upon 
the  number,  situation,  and  connection  of  its  stamens  and 
pistils.  Such  a  system  furnishes  an  easy  mode  of  as- 
certaining the  names  of  plants,  just  as  the  alphabetical 
arrangement  of  words  in  a  dictionary  is  the  easiest  way 
of  enabling  one  to  find  any  word  that  he  wants.  But 
the  arrangement  is  artificial   and   arbitrary,  the   number 


THEIR   QUALITY.  83 

and  relative  situation  of  the  stamens  and  pistils  in  a  plant 
no  more  determining  its  leading  and  essential  character- 
istics, than  the  significance  and  mutual  relations  of  words 
depend  upon  the  position  which  their  initial  letters  happen 
to  occupy  in  the  alphabet.  In  the  Natural  System,  these 
prominent  and  essential  attributes  of  plants  are  made  to 
mark  out  the  classes  into  which  they  are  divided,  and 
thus  the  relations  which  actually  exist  between  the  things 
themselves  stand  out  with  the  same  relative  prominence 
in  the  thoughts  wherein  they  are  represented  to  conscious- 
ness. The  Concepts  here  not  only  denote  their  objects, 
but  represent  them  in  a  manner  which  approximates,  though 
distantly,  the  fulness  of  Intuition. 

The  three  merits  of  Clearness,  Distinctness,  and  Ade- 
quacy, which  constitute  the  Quality  of  a  Concept,  pre- 
suppose a  reference  to  some  standard,  which,  for  the  very 
reason  that  it  is  a  standard,  must  be  independent  of  our 
Thought,  —  that  is,  not  subject  to  arbitrary  change  in 
Thought.  Strictly  speaking,  every  Concept  considered 
merely  as  such,  or  as  an  individual  Thought  in  conscious- 
ness, must  have  its  own  degree  of  each  of  these  merits, 
and  cannot  change  this  degree  without  becoming  a  dif- 
ferent Concept  from  what  it  was.  Whatever  faults  may 
be  imputed  to  it  when  it  is  compared  with  some  standard, 
it  may  still  be  said  of  it,  even  in  its  present  state,  that 
it  connotes  something  and  denotes  something,  and  thus 
has  all  the  essential  characteristics  which  enter  into  our 
definition  of  a  Concept.  Any  change  to  which  it  may 
be  subjected  is  not  an  improvement  of  this  Concept,  but 
the  substitution  of  another  in  its  place,  having  different 
Marks,  and  therefore  denoting  not  the  same  objects  as 
before.  Such  a  change  or  substitution  can  be  required 
only  through  a  reference  in  Thought  to  some  standard,  to 
which  this  Concept,  or  the  Concept  as  it  now  stands, 
does  not  conform,  but  to  which  it  was  previously  implied 
that  it  ought  to  conform. 


84  THE  DOCTRINE  OF  CONCEPTS. 

There  are  two  standards,  one  of  the  name  and  the  other 
of  the  thing,  to  one  or  the  other  of  winch  every  Concept 
which  the  mind  can  form  is,  at  least  tacitly,  referred. 
"Words,  which  are  the  names  of  Concepts,  are  the  means 
of  communicating  our  Thought  to  others ;  and  they  cannot 
perform  this  office  unless  they  have  the  same  signification 
to  the  hearer  as  to  the  speaker ;  that  is,  each  name  must 
call  up  the  same  Concept  in  the  minds  of  both.  A  Con- 
cept may  be  faulty,  then,  not  as  a  Concept,  (for  in  this 
respect,  or  in  reference  to  the  mere  Form  of  Thought, 
one  Concept  is  as  good  as  another,)  but  because  it  has  a 
wrong  name,  whereby  it  improperly  assumes  to  be  the  same 
Thought  which  is  designated  by  that  name  in  the  minds  of 
other  persons*  generally.  Thus  it  is  that  language,  among 
its  other  offices,  has  an  important  influence  in  the  regula- 
tion and  fixation  of  Thought.  We  do  not  classify  things 
and  form  Concepts  of  them  arbitrarily,  each  one  according 
to  his  own  preferences;  but  the  necessity  of  maintaining 
intercourse  with  other  minds  imposes  on  us  a  constant 
effort  to  approximate  our  Thoughts  to  theirs, — that  is, 
to  the  Thoughts  which  they  have  fixed  and  established 
for  general  use  through  stamping  upon  them  certain  names. 
The  Thoughts  which  I  attach  to  the  words  church,  state, 
government,  for  instance,  may  be  as  correct  and  proper, 
in  themselves  considered,  as  the  connotation  which  you 
attach  to  them ;  but  it  is  a  decisive  objection  to  my  mode 
of  thinking,  if  I  attach  these  old  and  familiar  names  to 
peculiar  combinations  of  Thought  which  they  never  before 
designated,  and  to  which  people  generally  do  not  now 
give  these  appellations.  Owing  to  the  symbolic  use  of 
language,  in  which,  as  already  explained,  words  are  em- 
ployed as  temporary  substitutes  for  Thoughts,  we  are 
continually  learning  and  using  words  before  we  have  fully 
learned  their  meaning.  Gradually,  by  a  process  of  in- 
duction; we  accommodate  our  use  of  these  words  to  their 


THEIR   QUALITY.  85 

established  usage ;  and  it  is  while  thus  learning,  that  our 
Thoughts  are  said  to  be  wanting  in  Clearness,  Distinctness, 
and  Adequacy.  In  truth,  it  is  not  our  Thoughts  which 
are  thus  faulty,  but  our  apprehension  of  other  people's 
Thoughts,  or,  what  is  the  same  thing,  of  the  meaning 
which  they  attach  to  certain  words.  My  own  Concepts 
of  church,  state,  &c.  are  Clear  and  Distinct  enough,  unless 
indeed  I  now  hear  these  words  for  the  first  time ;  but  I 
cannot  clearly  distinguish  what  I  imperfectly  understand 
to  be  your  Concepts  of  them  from  certain  other  kindred 
or  nearly  allied  Thoughts;  or  I  have  but  an  Indistinct 
knowledge  of  the  several  Marks  which  are  connoted  in 
the  Concepts  which  you  and  other  men  have  of  them  j 
or  my  connotation  of  these  Marks  is  Inadequate,  —  that 
is  to  say,  not  so  full  as  other  people's. 

The  second  standard  to  which  our  Concepts  are  referred, 
when  they  are  said  to  be  deficient  in  Quality,  is  the  class 
of  things  which  they  denote,  and  which  they  consequently 
ought  to  represent  as  perfectly  as  possible.  Thus,  every 
artisan,  through  long  use,  has  a  more  Adequate,  Clear, 
and  Distinct  Concept  of  each  of  the  tools  of  his  trade, 
each  of  the  objects  which  he  works  upon,  and  each  of  the 
processes  to  which  these  objects  are  subjected,  than  it  is 
possible  for  other  persons  to  possess  who  have  no  special 
familiarity  with  the  business.  The  Concepts  which  these 
other  persons  have  may  be  perfect  enough  for  the  correct 
use  of  language ;  that  is,  they  may  apply  the  technical 
names  rightly.  But  when  compared  with  the  full  and 
accurate  Notions  which  have  been  acquired  by  experts, 
they  appear  to  be,  as  they  are,  very  imperfect  representa- 
tions of  the  things  themselves. 

The  difference  between  these  two  standards  to  whijh  all 
Concepts,  in  respect  to  their  Quality  or  degree  of  perfec- 
tion, are  referred,  enables  us  to  understand  the  distinction 
wliich  logicians  long  ago  established  between  nominal  and 


86  THE  DOCTRINE  OF  CONCEPTS. 

real  Definitions.  This  distinction  has  been  very  imperfectly 
apprehended  by  many,  especially  by  those  who,  unable  to 
find  any  other  mode  of  distinguishing  the  two  sorts  of 
definition,  have  held  that  a  Nominal  one  consisted  only  in 
explaining  the  meaning  of  the  word  by  synonymes,  or  by 
unfolding  its  etymology.  Such  a  process  would  be  Gram- 
matical rather  than  Logical;  rightly  considered,  it  is  no 
definition  at  all.  A  Nominal  Definition  is  the  distinct 
explication  of  all  the  Marks  which  are  connoted  in  the  name 
of  the  Concept  by  general  consent,  as  evinced  in  the  use 
of  language.  But  language  is  imperfect,  and  words  in 
common  use  often  signify  much  less  than  exact  science 
requires.  A  Real  Definition  is  a  distinct  explication  of 
all  those  Marks,  and  those  only,  which  a  careful  examination 
of  the  class  of  things  denoted  by  the  word  proves  to  be  both 
Original  and  Essential.  It  is  obvious  that  the  Nominal 
and  the  Real  Definition  of  a  Concept  will  often  coincide. 
This  is  usually  the  case  with  the  technical  terms  in  every 
science,  especially  those  of  recent  origin,  whose  connota- 
tions are  usually  determined  with  great  care  before  their 
names  are  invented.  In  other  cases,  as  already  explained, 
the  two  definitions  may  differ  very  widely  from  each  other. 
The  further  consideration  of  Definition,  and  of  Division 
also,  as  the  subsidiary  processes  by  which  the  Quality  of 
Concepts  may  be  improved,  must  be  postponed  till  after 
we  have  treated  of 

3.     The  Relations  of  Concepts. 

The  Relation  of  Concepts,  as  already  remarked,  is  a 
technical  phrase,  which  is  understood  to  mean  their  Re- 
lations to  each  other  only,  and  not  to  the  other  forms  of 
Thought,  which  will  be  considered  hereafter. 

A  series  or  hierarchy  of  Concepts,  formed  by  successive 
steps  of  Generification,  like  the  one  given  in  the  table  on 


THEIR  RELATIONS.  87 

page  72,  represents  a  succession  of  Concepts  as  subordi- 
nated to  each  other  in  their  two  Quantities  of  Extension 
md  Intension.  But  the  names  of  the  Second  Intentions, 
which  express  the  Relations  of  these  Concepts  or  classes 
\o  each  other,  are  given  with  primary  reference  to  the 
Extension  only.  Unless  express  notice  is  given  to  the 
tontrary,  therefore,  we  shall  always  speak  only  of  their 
Relation  in  Extension.  Of  any  two  Concepts  in  such  a 
6eries,  that  one  is  called  the  Superior,  Higher,  or  Broader, 
which  has  the  greater  Extension,  —  that  is,  which  de- 
notes the  larger  number  of  individual  objects ;  it  may 
also  be  called  the  Superordinate.  The  other,  having  less 
Extension,  or  denoting  fewer  Individuals,  is  called  In- 
ferior, Lower,  Narrower,  or  Subordinate,  Thus,  referring 
to  the  table  again,  animal  is  Superior  or  Superordinate  to 
mammal,  which,  as  included  under  it,  or  denoting  fewer 
individuals,  is  called  Inferior  or  Subordinate.  The  Supe- 
rior, also  as  the  more  general  notion,  and  as  obtained  by 
the  process  of  Generification  or  throwing  out  Marks,  is 
called  the  Genus ;  while  the  Inferior,  as  more  specific,  and 
obtained  by  the  process  of  Specification,  or  thinking  in 
Marks,  is  called  the  Species.  These  names  being  merely 
relative,  it  is  evident  that  the  same  Concept  is,  at  the 
same  time,  a  Genus  to  any  lower  Concept,  and  a  Species 
to  any  higher  one. 

The  Highest  or  Broadest  Concept  in  such  a  series, 
denoting  most  individuals  and  connoting  fewest  Marks,  is 
called  the  Summum  Genus ;  hence,  it  is  defined  by  logi- 
cians to  be  a  Genus  which  cannot  become  a  Species.  On 
the  other  hand,  the  lowest  Concept  in  the  series,  as  denot- 
ing the  least  and  connoting  the  most,  is  called  an  Infima 
Species.  In  fact,  it  denotes  individuals  only,  and  not  any 
classes  or  Species  of  individuals ;  therefore  it  is  defined  to 
be  a  Species  which  cannot  become  a  Genus.  Each  interme- 
diate Concept,  as  we  have  just  said,  is  a  Species  to  those 


88  THE  DOCTRINE   OF   CONCEPTS. 

above  it,  and  a  Genus  to  those  below  it.  Its  next  Higher 
neighbor  is  called  its  proximate  Genus ;  and  its  next  lower 
one  might  be  termed  a  proximate  Species,  though  this  term 
is  not  in  frequent  use. 

When  the  name  of  any  Higher  Concept  is  applied  as  the 
name  of  a  Lower  one,  or  of  an  individual,  it  is  called  its 
abstract  name,  or  its  denomination  in  the  abstract ;  the  pecu- 
liar or  proper  appellation  of  this  lower  Concept  or  indi- 
vidual is  called  its  concrete  name.  Thus,  animal  is  an 
Abstract,  and  man  the  Concrete,  name  of  a  rational  animal; 
and  again,  relatively,  man  is  the  Abstract,  and  John  the 
Concrete,  appellation  of  the  individual,  this  man  whom  we 
are  speaking  of.  These  names  obviously  have  reference 
to  the  Intension  of  the  Concept,  the  Abstract  name  being 
obtained  by  Abstraction,  that  is,  by  throwing  out  Marks, 
and  the  Concrete  signifying  all  the  Marks  taken  together 
(con-cresco,  grown  together),  or  the  whole  Intension. 

According  to  another  and  more  frequent  use  of  language, 
an  "  Abstract  name  "  has  a  narrower  signification  than  the 
one  here  indicated,  being  applicable  only  to  one  peculiar 
Species  of  Higher  Concept,  instead  of  denoting  the  Abstract 
use  of  any  Higher  Concept  whatever.  What  appears  only 
as  a  Mark  of  the  Concept  in  its  Lower  or  Concrete  use,  is 
itself  a  Higher  Concept ;  and  if  its  denotation  is  then 
altered,  —  that  is,  if  it  no  longer  denotes  things  as  before, 
but  only  various  kinds  and  degrees  of  that  attribute  which 
the  Concrete  term  connotes,  —  it  is  then,  and  then  only, 
commonly  called  an  Abstract  term.  Thus,  to  recur  to  the 
instance  already  given,  man  connoting  rational  animal,  we 
may  take  rational  instead  of  animal  as  the  Higher  Con- 
cept ;  and  then,  altering  its  denotation,  we  may  understand 
it  to  mean,  not  rational  beings,  but  various  kinds  and  de- 
grees of  rationality.  Hence,  such  terms  as  rationality, 
redness,  whiteness,  humanity,  &c.  are  called  Abstract 
names.     According  to  this  use,  an  Abstract  term  is  ono 


THEIR  RELATIONS. 


89 


which  denotes  that  which,  in  its  Concrete  application,  it  con- 
noted; it  is  a  Mark  or  attribute  considered  as  a  thing. 

The  Relations  thus  far  explained,  as  arising  from  the 
higher  or  lower  position  of  a  Concept  in  the  series  or 
hierarchy  to  which  it  belongs,  are  all  denominated  Rela- 
tions of  Subordination,  They  may  be  aptly  symbolized  by 
p,  series  of  concentric  circles,  thus :  — 

Here,  A,  having  the  greatest 
extent,  and  so  containing  all  the 
others  under  it,  represents  the 
Summum  Genus  ;  while  F,  as 
least  extended,  and  denoting 
only  individuals,  fiot  classes, 
represents  the  Infima  Species. 
Any  intermediate  circle,  C,  is  a 
subaltern  Genus  or  Species,  be- 
ing Genus  to  D  and  Species  to  B. 
If  we  were  to  use  the  same  diagram  to  symbolize  the 
Relations  of  Intension,  since  the  two  Quantities  are  in 
inverse  ratio  to  each  other,  the  order  of  the  letters  would 
be  reversed.  F,  as  connoting  the  most  Marks  or  having 
the  largest  Intension,  would  be  the  outermost  circle,  and 
A,  having  the  least  Intension,  would  be  the  innermost  or 
smallest. 

In  general,  and  for  practical  purposes,  the  terms  Sum- 
mum  Genus  and  Infima  Species  are  applied  not  in  an 
absolute,  but  only  in  a  relative  sense  ;  —  relative,  that  is, 
not  to  the  totality  or  the  smallest  class  of  all  conceivable 
things,  but  to  the  totality  or  the  smallest  convenient  class  of 
those  things  only  which  we  are  now  thinking  of;  say,  all  the 
objects  of  some  particular  science.  Thus,  in  Zoology,  ani- 
mal is  considered  as  the  Summum  Genus,  no  notice  being 
taken  of  vegetables  and  minerals ;  and  what  is  usually 
termed  a  "Variety"  or  "Sub- Variety"  —  King  Charles 
Spaniel,  for  instance  —  is  an  Infima  Species. 


90  THE  DOCTRINE  OF  CONCEPTS. 

Absolutely  speaking,  logicians  maintain  that  Summum 
Genus  and  Infima  Species  are  both  unattainable,  —  that 
they  are  limits  of  classification  in  Thought,  which  we  can 
approximate,  but  never  reach.  They  express  this  impossi- 
bility under  the  form  of  two  Laws  of  Thought.  The  first 
of  these,  called  the  Law  of  Homogeneity,  affirms  that  things 
the  most  dissimilar  must,  in  some  respects,  be  similar  or 
homogeneous  ;  and  consequently,  any  two  Concepts,  how 
unlike  soever,  may  still  both  be  subordinated  under  some 
higher  Concept.  Thus,  animals  and  vegetables,  distinct  as 
they  are  from  each  other,  are  both  contained  under  the 
higher  Concept  organized  natural  objects.  And  even  from 
tliis  connotation,  if  we  subtract  the  Mark  organized,  the  re- 
mainder will  be  a  still  higher  Concept,  natural  objects,  which 
will  include  minerals,  as  well  as  animals  and  vegetables. 

On  this  ground,  Mr.  Mansel  and  other  logicians  main- 
tain that  thing  or  entity,  connoting  but  one  attribute,  exist- 
ence (real  or  imaginary),  which  would  seem  to  be  an 
absolute  Summum  Genus,  is  not  thinkable.  They  deny 
that  it  is  a  possible  object  of  Thought,  on  the  ground  seem 
ingly  that  it  does  not  contain  a  plurality  of  attributes. 
But  as  reasons  have  already  been  assigned  (page  61)  why 
a  Concept,  as  actually  thought  by  us,  may  have  only  one 
attribute  or  distinguishing  Mark,  I  cannot  see  why  ens  is 
not  thinkable,  as  distinguished  from  nihil,  which  has  not 
even  this  one  attribute  of  (real  or  imaginary)  existence,  and 
is  therefore  certainly  not  conceivable.  That  it  is  a  veiy 
vague  and  indefinite  Thought,  is  admitted ;  this  is  a  conse- 
quence of  its  connotation  being  reduced  to  a  minimum. 
But  to  say,  that  "  distinguishable  from  nothing  "  is  tanta- 
mount to  affirming  that  it  is  not  distinguishable  at  all,  seems 
to  me  in  this  connection,  or  for  the  purposes  of  pure 
Thought,  a  mere  quibble.  I  can  certainly  think  a  differ- 
ence —  that  is,  a  relation  —  between  being  and  no-being, 
though  only  one  term  of  the  relation  is  positive,  and  the 


THEIK   RELATIONS.  91 

other  is  merely  negative.  The  algebraist  finds  a  very  dis- 
tinct relation  between  plus  a  and  minus  a,  as  the  presence 
of  one  in  place  of  the  other  affects  the  results  of  his  calcu- 
lation very  sensibly ;  and  both  these  expressions  are  clearly 
distinguishable  from  zero.  It  is  too  much  of  a  paradox  to 
affirm  that  there  is  no  difference  in  Thought  between  some- 
thing and  nothing. 

About  the  second  principle,  called  the  Law  of  Heteroge- 
neity, there  is  no  dispute.  According  to  this  Law,  things  the 
most  similar  must,  in  some  respects,  be  dissimilar  or  hetero- 
geneous ;  and  consequently,  any  Concept,  however  large 
its  Intension  may  be,  may  still  have  that  Intension  in- 
creased, without  thereby  descending  to  individuals.  What 
is  relatively  an  Infima  Species,  or  considered  as  such  for 
the  purposes  of  some  particular  science,  may  be  again  sub- 
divided into  two  or  more,  and  so  on  indefinitely.  Thus, 
King  Charles  Spaniel  may  be  subdivided  into  such  Spaniels 
9ne  year  old,  and  those  of  two  years  or  older;  into  those 
born  in  Europe,  and  those  born  in  America  ;  into  those  above, 
and  those  below,  three  pounds  in  weight,  &c.  Though,  as 
Mr.  Mansel  remarks,  "  as  far  as  the  Laws  of  Thought  are 
concerned,  it  is  permitted  to  unite  in  an  act  of  conception 
all  attributes  which  are  not  contradictory  of  each  other,  it 
is  impossible  in  practice  to  go  beyond  a  very  limited  num- 
ber. The  number  of  attributes  in  the  universe  not  logically 
repugnant  to  each  other  is  infinite  ;  and  the  mind  can  there- 
fore find  no  absolute  limits  to  its  downward  progress  in  the 
formation  of  subordinate  notions."  * 

The  Relation  of  Co-ordination  exists  between  different 
Species  which  have  the  same  Proximate  Genus;  two  or 
more  Species  are  thus  said  to  be  Co-ordinate  when  each 
excludes  the  other  from  its  own  Extension,  but  both  or  all 
are  included  under  the  Extension  of  the  same  nearest 
Higher  Concept.     For  instance,  dog,  wolf,  cat,  lion,  bear, 

•  Prolegomena  Logica,  p.  169. 


92  THE  DOCTRINE  OF  CONCEPTS. 

&c.  are  Co-ordinate  Species  under  the  same  Genus,  Car* 
nivora  ;  each  excludes  the  other,  —  what  is  wolf  is  not  cat, 
—  but  all  alike  are  Carnivora.  As  the  two  Quantities  of  a 
Concept  are  in  inverse  ratio,  and  as,  in  reference  to  Ex- 
tension, the  Species  is  contained  under  the  Genus,  so,  in 
reference  to  Intension,  the  Genus  is  contained  in  the  Spe- 
cies. Thus,  the  Intension  of  every  Species  contains  the 
Genus,  —  that  is,  the  aggregate  of  Marks  which  charac- 
terize the  Genus,  —  and  the  Specific  Difference,  —  that  is, 
the  aggregate  of  Marks  by  which  this  Species  is  distin- 
guished both  from  the  Genus  to  which  it  is  Subordinate, 
and  from  the  other  Species  with  which  it  is  Co-ordinate. 
Man  is  a  rational  animal: — here,  animal  expresses  the 
Genus  to  which  man  belongs,  and  rational  is  the  Specific 
Difference  whereby  man  is  distinguished  from  other  Species 
of  animals. 

Two  things  may  be  said  to  be  generieally  different,  when 
they  belong  to  different  Genera ;  specifically  different,  when 
they  belong  to  different  Species ;  individually  or  numeri- 
cally different,  when  they  do  not  constitute  one  and  the 
same  reality.  But  as  every  member  of  the  hierarchy, 
except  the  highest  and  the  lowest,  may  be  viewed  indif- 
ferently as  either  Genus  or  Species,  generic  difference  and 
specific  difference  are  only  various  expressions  for  the  same 
thing. 

"Individual  existences,"  as  Krug  remarks,  "can  only 
be  perfectly  discriminated  by  external  or  internal  Percep- 
tion, and  their  numerical  differences  are  endless ;  for  of 
all  possible  Contradictory  attributes,  the  one  or  the  other 
must,  on  the  principles  of  Contradiction  and  Excluded 
Middle,  be  considered  as  belonging  to  each  individual 
thing.  On  the  other  hand,  Species  and  Genera  may  be 
perfectly  discriminated  by  one  or  few  characters.  For 
example,  triangle  is  distinguished  from  every  Genus  or 
Species  of  geometrical  figures  by  the  single  character  of 


THEIR  DEFINITION  AND  DIVISION.  98 

trilaterality.  It  is,  therefore,  far  easier  adequately  to  de- 
scribe a  Genus  or  Species  than  an  Individual ;  as,  in  the 
latter  case,  we  must  select,  out  of  the  infinite  multitude 
of  characters  which  an  Individual  comprises,  a  few  of  the 
most  prominent,  or  those  by  which  the  thing  may  most 
easily  be  recognized."  We  may  describe,  but  cannot  define, 
an  Individual,  as  there  would  be  no  end  to  the  enumera- 
tion of  its  peculiar  attributes.  In  such  case,  the  only 
adequate  definition  is  a  view  —  an  Intuition  —  of  the  thing 
itself.      Omnis  intuitiva  notitia  est  definitio. 

The  other  Relations  of  Concepts  to  each  other  may  be 
very  briefly  indicated.  Concepts  are  said  to  intersect, 
when  the  Extension  of  one  coincides  in  part,  and  only  in 
part,  with  the  Extension  of  the  other.  Thus,  Frenchman 
and  Protestant  are  Intersecting  Concepts,  for  some  French- 
men are  Protestants  and  some  are  not,  some  Protestants 
are  Frenchmen  and  some  are  not.  These  may  be  sym- 
bolized by  two  circles  whose  circumferences  cut  or  intersect 
each  other.  Exclusive  Concepts  —  animal  and  vegetable, 
for  instance  —  do  not  coincide  in  any  part  of  their  Ex- 
tension, and  may  therefore  by  symbolized  by  two  circles 
which  lie  wholly  apart  the  one  from  the  other.  Recip- 
rocating, Convertible,  or  Coextensive  Concepts  are  those 
which  have  precisely  the  same  Extension,  as  living  being 
and  organized  being,  since  everything  which  lives  is  or- 
ganized. Two  circles  of  the  same  diameter,  and  laid  one 
upon  the  other  so  as  to  coincide  throughout,  would  aptly 
represent  Convertible  Concepts. 

4.     Definition  and  Division. 

It  has  already  been  said,  that  a  Concept  is  internally 
Distinct  when  we  can  fully  enumerate  and  clearly  distin- 
guish from  each  other  all  its  original  and  essential  Marks. 
The  process  through  which  this  is  accomplished  is  called 


9-1  THE   DOCTRINE   OF   CONCEPTS. 

Definition.  Again,  a  Concept  is  externally  Distinct  when 
we  can  fully  enumerate  all  its  subordinate  Genera  and 
Species.  Tliis  process  is  called  the  Division  of  the  Con- 
cept. Both  processes  have  reference  to  one  or  the  other 
of  the  two  standards,  —  the  name  and  the  thing,  —  bj 
which  it  is  determined  whether  the  Concept  in  our  minds 
is,  what  it  purports  to  be,  a  faithful  copy  or  representation 
of  what  is  generally  designated  by  that  name,  or  a  full 
enumeration  of  the  original  and  essential  attributes  of  the 
class  of  things  so  designated.  We  will  first  consider 
Definition  of  names  only,  Division  relating  only  to  classes 
of  things,  the  object  of  both  processes  being  not  to  de- 
termine and  render  distinct  the  Concepts  which  we  already 
possess,  but  to  substitute  others  for  them  which  shall  more 
perfectly  answer  our  purposes.  The  Concept  to  be  defined 
should  be  called  the  definiendum,  the  Definition  itself 
being  the  definientia. 

A  Definition  consists  primarily  of  two  parts,  the  Proxi- 
mate Genus  and  the  Specific  Difference  of  the  Concept 
defined;  for  these  two  elements,  as  we  have  just  seen, 
make  up  the  whole  Intension  of  every  class.  Thus, 
carnivor  is  a  flesh-eating  mammal;  the  word  mammal  here 
denotes  the  Proximate  Genus,  and  flesh-eating  the  Specific 
Difference  which  distinguishes  camivora  from  other  mam- 
mals. Such  a  Definition,  however,  is  incomplete,  as  it  is 
further  necessary  to  define  the  Genus  which  makes  a  part 
of  it ;  and  this  can  be  done  only  by  considering  this  Genus 
(mammal)  as  a  Species,  and  assigning  to  it  its  own  Proxi- 
mate Genus  (the  next  higher  one  in  the  hierarchy),  ani- 
mal, and  its  Specific  Difference,  suckling  its  young.  We 
proceed  in  this  manner  till  we  have  reached  the  Summum 
Genus,  each  Specific  Difference  successively  taken  up  be- 
ing the  Mark  which  was  abstracted  in  the  original  process 
of  Generification,  and  the  sum  of  these  Differences  being, 
therefore,  the  aggregate  of  all  the  Marks  which  make  up 


THEIR  DEFINITION  AND  DIVISION.  95 

the  Intension  of  the  Concept  first  proposed  to  be  defined. 
What  may  be  called  the  secondary  or  proper  Definition, 
then,  as  before  stated,  is  the  distinct  explication  of  all  the  I 
Marks  which  are  connoted  in  the  name  of  the  Concept. 
Thus,  having  successively  defined  dog  as  camivor,  camivor 
as  mammal,  mammal  as  animal,  and  animal  as  thing, 
annexing  in  each  case  the  corresponding  Specific  Differ- 
ence, we  then  sum  up  all  these  Specific  Differences,  and 
thus  form  the  proper  Definition  consisting  solely  of  these 
Differences,  —  that  is,  of  all  the  Marks  which  the  de- 
finiendum  connotes.  Hence  it  appears,  that  though  the 
defining  analysis  is  of  the  Intension  only,  yet  it  is  regu- 
lated by  the  Extension,  as  the  Extension  determines  the 
order  in  which  the  Intension  is  resolved  into  the  Marks 
which  are  its  elements. 

It  is  obvious  also,  that  Definition  by  Genus  and  Specific 
Difference  in  all  its  successive  steps  supposes  a  previous 
knowledge  of  the  whole  hierarchy  of  Concepts  through 
which  it  ascends,  and  therefore  it  only  explicitly  enu- 
merates the  Marks  which  were  already  implicitly  known. 
The  Classification  here  precedes,  and  is  the  means  through 
which  we  form,  the  Definition.  Usually,  however,  we 
proceed  in  the  inverse  order  of  this  process :  we  seek  first 
for  the  Definition,  —  that  is,  for  a  knowledge  of  all  the 
original  and  essential  attributes  of  a  class  of  things,  —  as 
a  preliminary  step  towards  determining  the  Classification, 
or  assigning  the  class  to  its  proper  place  in  a  hierarchy 
of  Concepts.  Here,  the  Definition  is  primarily  of  the 
thing,  and  only  secondarily  of  the  name,  the  problem  be- 
ing how  to  determine  the  sum  of  the  original  and  essential 
characteristics  of  this  class  of  things.  The  following  are 
the  Rules  usually  given  by  Logicians  for  the  solution  of 
this  problem,  —  that  is,  for  the  proper  formation  of  Defi- 
nitions. 

1.  A  Definition  must  be  adequate ;  that  is,  it  must  have 


96  THE  DOCTRINE  OF  CONCEPTS. 

precisely  the  same  Extension  as  the  thing  defined.  If 
not,  if  the  Predicate  defining  denotes  more  objects  than  the 
Subject  defined,  the  Definition  is  too  Wide ;  if  it  denote 
fewer  objects,  it  is  too  Narrow.  Thus,  when  a  triangle 
is  defined  "  a  figure  having  three  rectilinear  sides,"  the 
Definition  is  too  Narrow,  as  there  are  spherical  triangles 
to  which  it  will  not  apply.  If  we  say,  "  water  is  a  com- 
pound of  oxygen  and  hydrogen,"  the  Definition  is  too 
Wide,  as  it  includes  not  only  water,  but  something  else,  — 
a  deutoxide  of  hydrogen.  When  this  rule  is  complied 
with,  the  Definition  and  the  thing  defined  are  Reciprocat- 
ing or  Convertible  Concepts;  consequently,  eveiy thing 
to  which  the  Definition  applies,  and  nothing  to  which  it 
does  not  apply,  is  the  thing  defined.  When  this  is  the 
case,  our  Concept  of  this  class  of  things  has  become  per- 
fectly Clear,  or  distinguishable  from  all  other  Concepts. 

2.  The  Definition  must  not  be  tautological ;  that  is,  it 
must  not  contain  the  name  of  the  thing  defined,  as  this 
is  precisely  the  word  which  we  are  bound  to  explain.  It 
is  equally  a  violation  of  this  rule  to  allow  any  of  the 
derivatives  of  this  name,  or  any  of  its  correlative  notions, 
either  one  of  which  can  be  explained  only  through  the 
other,  to  constitute  a  part  of  the  definition.  This  fault  is 
called  "  defining  in  a  circle."  Lexicographers  often  fall 
into  it  unawares,  as  when  they  define  a  board  to  be  "  a  thin 
plank,"  and  then  a  plank  to  be  "  a  thick  board  "  ;  or  when 
they  say  that  life  is  "vitality,  the  state  of  being  alive, 
the  opposite  of  death." 

3.  A  Definition  ought  not  to  proceed  by  Negative  or 
Disjunctive  attributes,  when  it  is  possible  to  avoid  both. 
You  cannot  teach  me  what  a  notion  is,  by  merely  de- 
claring what  it  is  not,  or  that  it  is  one  of  several  things 
without  indicating  which  one  is  intended.  It  is  no  real 
Definition  to  say  of  parallels,  that  they  are  "lines  which 
do  not  meet,"  or  of  oxygen,  that  it  is  "  one  of  the  gases 


THEIR  DEFINITION  AND  DIVISION.  97 

fit  for  respiration."  But  convenience  often  requires  what 
Logicians  call  division  by  dichotomy,  in  which  a  Genus  ia 
divided  into  two  Species  having  Contradictory  Marks ;  that 
is,  one  of  these  Species  has,  and  the  other  has  not,  cer- 
tain well-defined  characteristics,  the  latter,  of  course,  being 
capable  only  of  Definition  by  negation.  Thus  Cuvier, 
having  determined  with  great  precision  the  attributes  of 
Vertebrated  animals,  found  it  convenient  to  regard  all 
other  animals  as  Invertebrates,  that  is,  as  not  possessing 
these  attributes. 

4.  A  Definition  must  be  precise,  —  that  is,  it  must  con- 
tain nothing  unessential  or  superfluous.  Thus,  all  Deriva- 
tive Marks  should  be  excluded  as  superfluous,  after  their 
Originals  have  been  enumerated;  for  they  are  virtually 
contained  in  those  Marks  from  which  they  are  deducible 
by  the  necessary  Laws  of  Thought,  so  that  the  mention 
of  them  only  cumbers  the  Definition  without  really  enlarg- 
ing it.  That  a  triangle  is  half  of  a  parallelogram,  is  no 
proper  part  of  the  Definition  of  a  triangle,  inasmuch  as 
it  is  a  necessary  consequence  of  this  figure  having  three 
sides  and  three  angles.  Unessential  attributes  are  also 
superfluous ;  that  man  is  a  featherless  biped  is  an  accident, 
not  an  essential  trait,  of  his  humanity.  Give  him  a  coat 
of  feathers,  and  he  is  still  man  ;  but  deprive  him  of  ration- 
ality, and  he  is  no  longer  human. 

5.  A  Definition  must  be  perspicuous;  for  we  define 
only  in  order  to  make  more  clear,  and  obscure  or  figurative 
expressions  do  not  conduce  to  this  end,  but  only  increase 
the  difficulty.  "  Tropes  and  figures,"  says  Krug,  "  are  log- 
ical hieroglyphics:  they  do  not  indicate  the  thing  itself, 
but  only  something  similar."  But  many  expressions,  origi- 
nally metaphorical,  have  ceased  to  be  so  through  long 
use  in  their  secondary  meaning.  Their  original  significa- 
tion has  become  obsolete,  and  no  longer  recurs  to  perplex 
us.     This   is   the   case  with  nearly  all  the  words  which 


y»  THE  DOCTRINE  OF   CONCEPTS. 

now  denote  mind  and  its  operations,  though  they  were 
first  applied  only  to  what  is  material. 

Dr.  Thomson  takes  a  wider  view  of  Definition,  as  in- 
cluding any  Predicate  which  may  be  "  useful  to  mark  out 
for  us  more  clearly  the  limits  of  the  subject  defined,  and 
is  therefore  capable  of  being  employed  as  a  Definition  for 
some  thinker  or  other."  "  Any  of  the  Predicates  we 
propose  to  include,"  he  continues,  "  though  not  the  absolute 
Definition,  not  the  Genus  and  Difference,  maVoe  em- 
ployed as  a  Definition  by  some  particular  perstfh,  and  may 
to  him  fulfil  the  purpose  of  the  best  logical  Definition 
which  can  be  given,  "  and  therefore  ought,  if  possible, 
to  be  comprehended  under  the  same  head."  In  conformity 
with  this  view,  he  enumerates  the  following  six  sources 
from  which  convenient  Definitions  may  arise. 

"i.  From  Resolution,  when  the  Marks  of  the  definitum 
are  made  its  definition ;  as  in  4  a  pension  is  an  allowance 
for  past  services.'  It  is  not  necessary  that  the  Marks 
should  be  completely  enumerated, — that  the  conception 
should  be  strictly  adequate,  —  but  only  that  the  Marks 
should  suffice  for  the  identification  of  the  Subject,  as  belong- 
ing to  it  all  and  to  it  alone ;  so  that  Aristotle's  Property 
would  be  included  in  it.  ii.  From  Composition,  the  reverse 
of  the  last  method,  in  which  the  definitum,  a  conception  of 
which  the  component  Marks  are  enumerated,  stands  Subject 
to  a  Definition  implicitly  containing  those  Marks ;  as,  l  those 
who  encroach  upon  the  property  of  others  are  dishonest.' 
iii.  From  Division,  where  we  define  the  Subject  by  enumer- 
ating its  Dividing  Members ;  as,  *  Britons  are  those  who 
dwell  in  England,  Scotland,  or  Wales.'  All  the  judg- 
ments called  disjunctives  are  under  this  head.  iv.  From 
Colligation,  the  exact  reverse  of  the  last ;  where  the  Divid- 
ing Members  of  a  conception  are  enumerated  in  the  Subject, 
and  the  divided  conception  itself  added  to  define  them ;  as, 
4  historical,  philosophical,  and  mathematical  sciences  are  the 


THEIR   DEFINITION   AND   DIVISION. 


99 


sum  (i.  e.  are  all,  or  equal)  of  human  knowledge.'  This 
is  the  form  which  Inductive  Judgments  naturally  assume. 
v.  From  change  of  Symbol,  where  both  Subject  and  Predi- 
cate are  symbolic  conceptions,  the  latter  being  given  as  a 
substitute  for  the  former  on  a  principle  of  expedience  only ; 
as,  '  probity  is  honesty.'  This  is  the  nominal  definition  of 
some  logic-books,  vi.  From  Casual  Substitution,  where 
one  representation  is  put  for  another  on  a  principle  of 
expedience  only,  as  serving  to  recall  the  Marks,  which 
both  possess  in  common,  more  readily  to  the  hearer's 
mind ;  as,  ( the  science  of  politics  is  the  best  road  to  suc- 
cess in  life ;  pleasure  is  the  opposite  of  pain.' 
"Table  of  Definition. 


By  its  In- 
tension (or 
Marks)  • 

By  its  Ex- 
tension (or 
Sphere) 

By     Acci- 
dental Co- 
incidence 


being  unfolded,  = 

being  reunited, 
being    divided, 


Resolution,  or 
Definition 
proper, 
ii.      Composition. 

iii.     Division. 


being  reunited,  =  iv.     Colligation 
of  a  Symbol, 


of  Notation, 


y.      Nominal  Defi- 
nition. 

vi.     Accidental  Defi- 
nition." 


As  absolute  Definition  resolves  the  Intension  of  a  Con- 
cept into  its  constituent  Marks,  so  Division  resolves  the 
Extension  into  its  constituent  Genera  and  Species.  In  its 
most  general  acceptation,  division  is  the  separation  of  any 
whole  into  its  parts.  But  Logical  Division,  with  which 
alone  we  are  here  concerned,  is  such  a  separation  of  a  Logi- 
cal Whole  only, — that  is,  of  a  class  containing  under  it  other 
classes,  which  are  regarded  as  its  parts.  An  individual 
is  so  called  (in-divido)  because  it  cannot  be  (logically) 
divided ;  the  process  of  cutting  it  apart  is  properly  called 
Partition,  not  Division.  The  Mathematical  or  Integral 
whole  is  such  an  individual,  and  can  be  sundered  into  its 


100  THE  DOCTRINE  OF  CONCEPTS. 

parts  only  by  Partition.  The  parts  of  an  Essential  or 
Physical  whole,  as  they  interpenetrate  and  inform  each 
other,  cannot  be  separated  at  all  except  in  Thought.  But 
a  Logical  whole  is  itself  a  creation  of  Thought,  formed 
out  of  lesser  wholes  of  the  same  kind,  into  which  it  can 
be  resolved  by  mental  analysis. 

By  Partition,  triangle  may  be  resolved  into  smaller  tri- 
angles, or  into  angles  and  sides ;  the  former  Partition  may 
be  actual,  while  the  latter  can  only  be  ideal, — that  is,  it 
is  possible  only  in  Thought.  By  Division,  on  the  other 
hand,  triangle  is  resolved  into  rectilinear  and  curvilinear 
triangles,  or  into  equilateral,  isosceles,  and  scalene  triangles, 
as  these  are  Species  comprehended  under  one  Genus. 

The  Genus  to  be  divided  is  called  the  divisum,  and 
the  constituent  Species  into  which  it  is  resolved  are  the 
dividing  members  (membra  dividentid).  Agreeably  to  the 
nature  of  a  hierarchy  of  Concepts,  the  parts  which  result 
from  such  a  Division  are  in  themselves  wholes  containing 
other  parts  under  them,  and  the  dividing  process  repeated 
upon  these  is  called  a  Subdivision.  The  same  Concept 
may  likewise  be  differently  divided  from  different  points 
of  view,  each  separate  analysis  proceeding  on  what  is 
technically  termed  its  own  fundamentum  divisionis,  or 
peculiar  Ground  of  Division.  Thus,  man  may  be  divided 
geographically  into  European,  Asiatic,  American,  &c. ;  or, 
in  reference  to  color,  into  white,  red,  and  black  men  ;  or, 
in  reference  to  religion,  into  Christians,  Mohammedans,  and 
Pagans;  —  local  position,  color,  and  religion  being  here 
the  successive  fundamenta  divisionis.  So  the  books  in 
a  library  may  be  arranged  either  according  to  size,  as 
folios,  quartos,  octavos,  &c. ;  or  according  to  the  languages 
in  which  they  are  written,  as  Latin,  French,  English, 
&c.  ;*or  according  to  the  subjects  of  which  they  treat,  as 
theological,  scientific,  historical,  &c.  Perhaps  the  most 
important    point   in   the  philosophy   of  the    Classificatory 


1HEIR   DEFINITION   AND   DIVISION.  101 

Sciences  is  the  right  selection  of  a  fundamentum  divisionis, 
or  Ground  of  Division.  > 

If  a  Division  has  only  two  parts  or  members,  it  is  called 
a  dichotomy ;  and  if  such  a  Dichotomy  is  exhaustive,  as  it 
should  be,  these  two  members  are  evidently  Contradictories 
of  each  other  ;  for  whatever  is  contained  in  one  is  thereby 
excluded  from  the  other,  and  the  two,  taken  together, 
constitute  the  whole.  Accordingly,  these  two  Dividing 
Members  can  always  be  expressed  under  the  formula  B 
and  not-B.  Thus,  in  dividing  triangle,  instead  of  calling 
the  two  members  rectilinear  and  curvilinear,  it  is  better 
to  denominate  them  rectilinear  and  non-rectilinear.  A 
Division  into  three  members  may  be  called  a  trichotomy ; 
into  many,  a  polytomy. 

Logicians  have  commonly  given  the  following  Rules  for 
the  proper  Division  of  a  Concept. 

1.  Each  Division  should  have  but  one  fundamentum 
divisionis,  by  which  every  part  of  the  process  is  regulated. 
The  intervention  of  more  than  one  Ground  of  Division 
in  the  same  process  is  the  Logical  fault  which  is  called  a 
Cross  Division.  Thus,  a  Division  of  man  into  European, 
American,  Negro,  and  Pagan  is  faulty,  because  the  Ground 
of  Division  for  the  first  two  Dividing  Members  is  local 
position;  for  the  third,  it  is  color ;  and  for  the  fourth,  it 
is  religion.  The  consequence  of  this  blunder  is,  that  the 
same  individual  might  be  contained  in  each  of  the  last 
three  Members ;  —  for  he  may  be  at  once  American,  Negro, 
and  Pagan.  Whatever  we  may  select  as  a  Ground  of 
Division,  it  must  evidently  be  a  Mark  or  attribute  of  the 
Divisum,  and  the  number  of  distinct  forms  or  varieties, 
under  which  this  attribute  appears  in  the  class  of  things 
to  be  divided,  will  determine  the  number  of  Dividing 
Members.  One  of  the  Dividing  Members,  however,  and 
but  one,  may  be  marked  only  by  the  absence  of  thia 
attribute. 


102  THE  DOCTRINE  OF  CONCEPTS. 

2.  The  Mark  selected  as  the  Ground  of  Division  should 
be  an  Essential  attribute  of  the  Divisum,  and  one  which 
has  as  many  Derivatives,  or  which  determines  as  many 
of  its  other  attributes,  as  possible ;  otherwise,  the  Division 
will  be  complex  and  purposeless.  Thus,  the  color  of  the 
hair  is  an  unessential  attribute  of  man ;  mankind  might 
be  divided  into  a  large  number  of  classes  in  this  respect, 
but  as  veiy  few  of  his  physical,  and  none  of  the  intellectual 
or  moral,  qualities  of  a  man  can  be  inferred  from  the  fact 
that  he  has  red,  brown,  or  black  hair,  the  Division  would 
be  useless.  On  the  other  hand,  a  classification  of  men 
according  to  their  nationality  or  race,  their  geographical 
position,  or  their  religion,  is  found  to  be  an  eminently 
fruitful  one,  as  many  of  their  other  attributes  are  found 
in  invariable  connection  with  these  leading  characteristics, 
bo  as  to  be  readily  determined  by  them.  The  purpose 
for  which  a  Division  is  made  often  determines  the  selection 
of  its  Ground.  Thus,  soldiers  may  be  conveniently  divided 
into  cavalry  and  infantry,  as  this  distinction  is  one  of  great 
moment  in  military  affairs ;  but  to  divide  men  in  general 
into  foot  and  horsemen  would  be  absurd. 

3.  No  Dividing  Member  must  by  itself  exhaust  the 
Divisum;  and  the  Dividing  Members,  taken  together, 
must  exhaust,  and  no  more  than  exhaust,  the  Divisum. 
As  the  Genus  and  the  Co-ordinate  Species  into  which  it 
is  divided  stand  to  each  other  in  the  relation  of  a  whole 
to  its  parts,  the  propriety  of  this  rule  is  manifest.  Man 
cannot  be  divided  into  rational  and  irrational,  for  the  one 
class  of  rational  beings  includes  all  men,  so  that  neither 
of  the  Dividing  Members  is  a  part,  or  the  result  of  a 
Division,  properly  so  called.  Again,  as  all  the  parts  are 
required  to  constitute  a  whole,  if  the  Co-ordinate  Species, 
taken  together,  do  not  exhaust  the  Genus,  the  Division  is 
obviously  imperfect ;  one  or  more  members  remain  to  be 
supplied.     If,  on  the  other  hand,  they  overlap  the  Genus, 


THEIR  DEFINITION  AND   DIVISION.  103 

there  is  somewhere  an  excess,  which  ought  to  be  sub- 
tracted and  referred  to  another  class.  Government  cannot 
be  divided  into  monarchical,  aristocratic,  and  democratic; 
as  there  is  a  fourth  class,  the  mixed.  The  old  Division 
of  the  science  of  language  into  Grammar,  Logic,  and 
Rhetoric  is  redundant,  as  Logic  is  concerned  with  the 
laws  of  thought  rather  than  of  utterance,  and  therefore 
properly  belongs  to  the  science  of  mind. 

4.  The  Co-ordinate  Species  into  which  a  Genus  is  di- 
vided must  be  reciprocally  exclusive;  that  is,  no  one  of 
them  must,  in  whole  or  in  part,  contain  any  other.  In 
order  to  ascertain  whether  this  rule,  the  propriety  of 
which  is  obvious,  has  been  complied  with,  Logicians  apply 
the  test  of  Dichotomy^to  which  any  other  Division,  how- 
ever complex,  may  be  reduced.  Thus,  all  the  Co-ordinate 
Species,  B,  C,  D,  E,  &c,  of  any  Genus,  A,  may  be  rep- 
resented under  any  one  of  the  formulas,  B  and  not-B  ;  C  and 
not-C ;  B  and  not-B,  &c.  If  the  Dividing  Members  are 
mutually  exclusive,  C,  D,  and  E  will  each  be  found  under 
not-B ;  B,  D,  and  E,  under  not-C ;  B,  C,  and  E,  under 
not-B ;  and  so  on.  This  rule  is  violated  in  a  Cross  Divis- 
ion, where,  as  we  have  already  seen,  the  same  individuals 
may  appear  under  two  or  more  of  the  Dividing  Members ; 
and  also  when  a  Member  of  a  Subdivision  is  improperly 
co-ordinated  with  the  Members  of  a  primary  Division. 
This  last  fault,  however,  is  properly  ranked  under  the  next 
following  rule.  The  ten  Categories  of  Aristotle  are  now 
generally  condemned  as  a  faulty  Division,  because  the 
last  six  of  them  are  only  subdivisions  of  the  fourth,  Relation. 
"  For  the  Category  where  is  the  relation  of  a  thing  to 
other  things  in  space ;  the  category  when  is  the  relation 
of  a  thing  to  other  things  in  time ;  action  and  passion 
constitute  a  single  relation,  —  that  of  agent  and  patient " ; 
&c. 

5.  A  Division  must  proceed  step  by  step,  in  regular 


104  THE  DOCTRINE  OF  CONCEPTS. 

order,  from  proximate  to  remote  differences,  not  over- 
leaping any  step  which  is  properly  intermediate.  In  other 
words,  each  Species,  as  it  appears  among  the  Dividing 
Members,  must  emerge  directly  from  the  Division  of  its 
own  Proximate  Genus.  Divisio  ne  fiat  per  saltum  vel  Ma- 
turn.  Even  the  ordinary  Division  of  all  natural  objects 
into  animals,  vegetables,  and  minerals  is  faulty  in  this  re- 
spect, its  three  Species  not  being  properly  co-ordinate,  as 
one  step  has  been  omitted.  The  primary  Division  should 
be  by  Dichotomy  into  organic  and  inorganic  things,  animals 
and  vegetables  appearing  subsequently  as  a  subdivision  of 
the  organic. 


THE  DOCTRINE   OF  JUDGMENTS. 


CHAPTER    V 


THE    DOCTRINE   OF  JUDGMENTS. 

1.  The  Predicates  and  the  Categories.  —  2.  The  Quantity,  Quality,  and  Re- 
lation of  Judgments  according  to  the  Aristotelical  Doctrine.  —  3.  The 
Harailtonian  Doctrine  of  Judgments.  —  4.  The  Explication  of  Propo- 
sitions into  Judgments. 


JUDGMENT  is  that  act  of  mind  whereby  the  rela- 
tion of  one  Concept  to  another,  or  of  an  individual 
thing  to  a  Concept,  is  determined,  and,  as  a  consequence 
of  such  determination,  that  two  Concepts,  or  the  individual 
thing  and  the  Concept,  are  reduced  to  unity  in  Thought. 
A  Judgment  expressed  in  words  is  a  Proposition,  the 
two  terms  of  the  Judgment  being  called  the  Subject  and 
Predicate  of  the  Proposition.  The  assertions,  iron  is  mal- 
leable, John  is  brave,  determine  a  relation  of  agreement 
between  the  two  terms  involved  in  each,  whereby  these 
two  are  conceived  as  one,  and  thus  expressed,  malleable 
iron,  brave  John.  On  the  other  hand,  the  Judgment, 
quadrupeds  are  not  rational,  determines  the  relation  of 
disagreement  between  the  two  Terms,  so  that  one  is  now 
denied  to  be  a  Mark  of  the  other,  or,  what  is  the  same 
thing,  the  negative  Mark,  irrational,  is  now  attached  to 
the  Concept,  quadruped. 

As  we  have  already  defined  a  Concept  to  be  a  repre- 
sentation of  one  or  more  objects  through  their  distinctive 
Marks,  it  is  evident  that  Judgment  is  the  process  through 
which  Concepts  are  formed.  In  fact,  to  judge  is  to  recog- 
nize a  particular  Mark  or  attribute  as  belonging,  or  not 

5* 


106  THE  DOCTRINE  OF  JUDGMENTS. 

belonging,  to  a  certain  object  or  class  of  objects.  The 
Judgment  is  not,  strictly  speaking,  a  comparison,  but  it 
is  the  mental  act  of  conjoining  or  disjoining  two  things 
which  results  from  a  previous  comparison  of  them  with 
each  other,  and  a  consequent  recognition  of  their  agree- 
ment or  disagreement.  Hence,  as  Hamilton  remarks, 
"every  Concept  is  a  Judgment  fixed  and  ratified  in  a 
sign " ;  and,  again,  "  a  Concept  may  be  viewed  as  an 
implicit  or  undeveloped  Judgment ;  a  Judgment  as  an 
explicit  and  developed  Concept."  Thus,  the  Concept 
man,  which  has  the  four  Marks  biped,  two-handed,  rational, 
animal,  is  the  combined  result  of  four  separate  Judgments 
which  affirmed  each  of  these  attributes  to  be  characteristic 
of  man.  Aristotle,  the  Father  of  Logic,  seems  to  have 
regarded  Judgments  as  the  primary  elements,  out  of 
which  Concepts  are  formed ;  for  his  whole  system  is  based 
upon  an  analysis  of  Judgments.  Modern  writers  have  pre- 
ferred, as  more  convenient,  and  at  least  equally  correct, 
the  view  which  has  here  been  taken,  that  Concepts  are 
the  elements  of  Judgments.  In  truth,  each  presupposes 
the  other.  If  it  be  asked  which,  in  the  order  of  the 
mind's  development,  comes  first,  the  answer  is,  neither; 
but  a  partial  and  confused  apprehension  of  a  thing,  which 
is  a  young  child's  substitute  for  a  Concept,  and  which  is 
first  cleared  up  by  a  succession  of  Judgments  producing 
Concepts  properly  so  called.  Judgment  is  not  arbitrary 
or  dependent  upon  the  will ;  I  must,  in  Thought,  affirm 
tha  union  or  the  separation  of  the  two  Terms,  according 
as  the  relation  of  agreement  or  disagreement  is  perceived 
to  exist  between  them.  Hence,  the  Judgment  is  always, 
at  least  subjectively,  true ;  the  Proposition,  which  is  only 
the  verbal  affirmation,  may  be  either  true  or  false,  accord- 
ing as  it  does,  or  does  not,  agree  with  the  mental  Judgment. 
The  mere  succession  or  coexistence  of  two  Thoughts  in 
the  mind  does  not  constitute  a  Judgment.     I  may  think 


THE  DOCTRINE   OF  JUDGMENTS.  107 

first  of  man,  and  then  of  animal ;  but  no  Judgment  takes 
place  until  I  affirm  in  Thought  a  perceived  relation  between 
them,  —  until  I  think  man  is  animal.  Such  a  relation  can- 
not be  perceived  between  them  unless  one  is  regarded  as 
an  attribute  or  determination  of  the  other ;  —  that  is,  one 
must  be  regarded  as  determining,  and  the  other  as  deter- 
mined. For  if  both  were  viewed  as  determining,  there 
would  be  nothing  determined  ;  and  both  cannot  be  deter- 
mined, unless  there  is  something  determining  them.  Hence 
there  are  three  necessary  parts  of  a  Judgment ;  —  first,  the 
Concept  or  thing  determined,  which  is  called  the  Subject ; 
secondly,  the  determining  or  attributive  notion,  which  is 
called  the  Predicate;  and,  thirdly,  that  which  expresses 
the  relation  of  determination  between  the  Subject  and  the 
Predicate  is  called  the  Copula.  The  Subject  and  Predicate 
are  called  the  Terms  (termini)  or  Extremes  of  the  Judg- 
ment ;  and  the  Copula  may  therefore  be  symbolized  as  a 
straight  line  connecting  the  two  points  which  are  its  Terms 
or  ends. 

Though  a  Judgment  necessarily  consists  of  two  Terms, 
it  is  nevertheless  a  single  act  of  mind.  There  is  a  separate 
act  of  mind,  whereby  I  perceive  or  conceive  each  of  the  two 
Terms  taken  separately  ;  but  it  is  only  one  act  by  which  I 
perceive  and  affirm  the  relation  between  these  two  Terms, 
and  thereby  unite  them  into  one  process  of  Thought. 

When  the  mental  Judgment  comes  to  be  expressed  in 
words  as  a  Proposition,  each  of  its  three  parts  does  not 
necessarily  appear  as  a  distinct  word.  The  idiom  of  lan- 
guage often  requires  or  enables  us  to  express  two,  or  even 
all  three,  of  them  by  a  single  word  ;  but,  in  accordance 
with  the  general  Postulate  of  Logic,  that  we  must  be  al- 
lowed to  express  all  that  is  implicitly  thought,  we  cannot 
deal  logically  with  the  Proposition  until  its  form  is  so  modi- 
fied as  to  allow  all  the  three  elements  to  appear  separately. 
Moreover,  as  has  been  already  remarked,  the  Copula  of  a 


108  THE  DOCTRINE  OF  JUDGMENTS. 

Judgment,  since  it  expresses  the  present  union  of  two 
thoughts  now  before  the  mind,  must  always  appear  as  the 
present  tense  of  a  verb,  —  usually  of  the  verb  to  be :  is  or 
is  not  is  commonly  regarded  as  the  only  distinctive  expres- 
sion of  the  logical  Copula.  Thus  the  Propositions,  the  sun 
shines  ;  pluit ;  cogito,  ergo  sum  ;  he  came  yesterday  ;  John 
will  arrive ;  if  reduced  to  their  logical  form  as  Judgments, 
must  be  thus  expressed:  the  sun  is  shining;  the  rain  is 
falling;  I  am  thinking,  therefore  I  am  existing ;  he  is  the 
person  who  came  yesterday  ;  John  is  he  who  will  arrive.  In 
each  of  these  cases,  all  that  precedes  the  Copula,  is  or  am, 
is  the  Subject,  and  all  that  follows  the  Copula  is  the  Predi- 
cate.*    The   substantive  verb,  when  used   as  a   Copula, 

*  Hence  we  perceive  how  unfounded  is  the  objection  which  has  been  mado 
to  the  science  of  Formal  Logic,  on  the  ground  that  it  does  not  expound  the 
whole  theory  of  reasoning,  because  it  furnishes  no  explanation  of  an  infer- 
ence so  obvious  as  this  :  — 

A  is  greater  than  B  ; 
therefore,  B  is  less  than  A. 

But  here  the  Predicate  is  not  B  or  A,  but  "  greater  than  B  "  and  "  less  than 
A  " ;  the  meaning  of  these  two  expressions,  therefore,  belongs  to  the  Matter 
of  Thought,  with  which,  as  a  logician,  I  have  nothing  more  to  do  than  with 
the  meaning  of  A  or  B  taken  alone.  That  these  two  expressions  have  a 
correlative  meaning,  is  a  fact  which  belongs  to  the  science  of  language  rather 
than  to  that  of  Thought.  Instead  of  regarding  one  of  them  as  an  inference 
from  the  other,  it  would  be  more  correct  to  say  that  the  two  are  equivalent 
statements  of  the  same  fact ;  they  express  one  relation  between  two  Con- 
cepts. That  two  lines  converge  from  A  to  B  is  only  another  way  of  saying 
that  the  same  two  lines  diverge  from  B  to  A  ;  there  is  but  one  thing  to  bo 
said,  though  there  are  two  modes  of  saying  it.  In  like  manner,  we  may  say, 
but  W3  do  not  argue,  that 

Socrates  is  the  husband  of  Xantippe  ; 
therefore,  Xantippe  is  the  wife  of  Socrates. 

God  alone  is  omnipotent ; 

therefore,  no  one  is  omnipotent  but  God. 
In  such  cases,  the  second  proposition  is  an  interpretation  of  the  preceding 
one,  not  an  inference  from  it.     We  learn  from  a  dictionary,  not  from  a 
treatise  on  Logic,  what  different  phrases  are  equivalent  statements  of  one 
and  the  same  Thought 


THE  DOCTRINE  OF  JUDGMENTS.  109 

never  means  exists  ;  but  the  idea  of  existence,  when  it  is 
intended  to  be  conveyed,  forms  the  Predicate.  He  is,  in 
the  sense  of  he  exists,  is  logically  interpreted,  he  is  existing, 
Fuit  Ilium  ;  Troy  is  that  which  has  been,  —  is  that  which 
exists  no  longer. 

Logicians  generally  maintain  that  the  Copula  is  precisely 
equivalent  to  the  mathematical  sign  of  equality.  In  many 
cases,  this  is  undoubtedly  true.  If  the  Predicate  is  simply 
a  definition  of  the  Subject,  or  if  the  Proposition  in  any 
manner  expresses  the  entire  equivalence  of  its  two  Terms, 
it  can  then  be  expressed  in  the  manner  of  an  equation. 
Thus,  Saltpetre  =  nitrate  of  Potash  ;  Alexander  =  the  son 
of  Philip.  But  the  two  Terms  of  a  Judgment  are  not 
always  convertible  or  equivalent.  What  is  thought  and 
expressed  is  always  a  relation  between  the  two  Terms,  but 
is  not  always  a  relation  of  equivalence  or  identity.  Some- 
times, as  in  a  negative  Judgment,  it  is  a  relation  of  disa- 
greement ;  sometimes  the  Predicate  expresses  merely  one 
attribute  of  the  Subject,  and  then  the  relation  is  that  of  a 
whole  to  its  part,  since  only  a  portion  of  the  Subject's  In- 
tension is  affirmed  of  the  Subject.  When  we  say,  the  apple 
is  red,  we  do  not  mean  apple  =  red,  but  only  that  a  red 
color  is  one  out  of  many  attributes  of  the  apple,  —  is  a  part 
of  its  Intension.  In  this  case,  the  Copula  signifies  rather 
possession,  to  have,  than  equality,  to  be.  The  form  of  the 
Judgment  as  thought  is,  the  apple  has  a  red  color  as  one  of 
its  many  attributes. 

It  is  evident,  then,  that  there  are  two  classes  of  Judg- 
ments, properly  distinguished  by  Dr.  Thomson  as  Substitu- 
tive and  Attributive.  In  Substitutive  Judgments,  the  sign 
of  equality  may  be  used  as  the  Copula ;  the  Predicate  is 
properly  identified  with  the  Subject,  or  made  convertible 
with  it,  and  therefore  every  attribute  of  the  one  may  also 
be  affirmed  of  the  other.  If  A  =  B,  then  every  a;  of  A 
is  also  x  of  B;  all  that  is  true  of  "Alexander''  is  also  true 


110  THE  DOCTRINE  OF  JUDGMENTS. 

of  "the  son  of  Philip."  But  if  the  Judgment  is  only  At- 
tributive, the  sign  of  equality  cannot  be  used;  the  two 
Terms  are  not  convertible,  and  consequently  it  cannot  be 
inferred  that  they  possess  the  same  attributes.  Sweetness 
or  sourness  is  a  quality  of  the  apple,  but  not  of  the  red 
color  which  belongs  to  the  apple. 

The  distinction  here  explained  is  a  valid  and  important 
one  in  respect  to  Judgments  considered  simply  as  such,  or 
as  mere  phenomena  of  Thought,  irrespective  of  any  use  to 
be  subsequently  made  of  them  in  reasoning  or  other  mental 
processes.  In  Attributive  Judgments,  the  Predicate  is 
actually  thought  only  connotatively,  as  a  Mark  or  attribute 
of  the  Subject,  and  not  denotatively,  as  the  name  of  a  class 
of  things.  And  hence  Mr.  Mill  is  led  to  maintain,  that 
such  Judgments  never  express  truths  of  classification,  and, 
therefore,  that  the  generally  received  doctrine  of  Predica- 
tion, that  it  consists  in  placing  something  in  a  class  or  ex- 
cluding something  from  a  class,  is  entirely  unfounded. 
"  When  I  say  that  snow  is  white"  he  argues,  "  I  may  and 
ought  to  be  thinking  of  snow  as  a  class  ;  but  I  am  certainly 
not  thinking  of  white  objects  as  a  class  ;  I  am  thinking  of 
no  white  object  whatever  except  snow,  but  only  of  that,  and 
of  the  sensation  of  white  which  it  gives  me." 

All  this  is  granted.  At  the  moment  of  forming  the  Judg- 
ment, white  is  not  consciously  before  the  mind  as  the  name 
of  a  class  of  things.  We  then  think  of  it  only  connotatively, 
—  only  as  a  Mark.  But  it  is  still  true  that  we  originally 
learned  the  meaning  of  the  word  white  not  only  as  a  Mark 
connoting  a  quality,  but  also  as  a  Concept  denoting  a  class 
of  things,  —  namely,  white  objects  ;  otherwise,  it  would  not 
be,  what  it  certainly  is,  a  Common  Name  of  snow,  milk, 
chalk,  and  many  other  things.  And  though  this  its  deno- 
tative meaning  —  its  Extension  —  is  not  consciously  before 
the  mind  when  it  is  used  as  a  Mark  or  as  a  Predicate,  it  is 
still  there  potentially,  and  must  be  brought  out  or  expressed 


THE  DOCTRINE   OF  JUDGMENTS.  Ill 

when  we  attempt  to  found  an  inference  upon  this  Judg- 
ment, or  to  employ  it  as  one  of  the  premises  in  a  syllogism. 
To  borrow  Mr.  Mill's  own  instance,  —  if  I  am  in  doubt 
whether  Chimborazo  is  snow-covered,  I  may  reason 
thus :  — 

All  mountains  of  a  certain  altitude,  and  whose  summits 
are  perpetually  white,  are  snow-covered. 

But  Chimborazo's  lofty  summit  is  always  white,  —  that 
is,  it  is  one  of  this  class  of  mountains. 

Therefore,  Chimborazo  is  snow-covered. 

As  already  observed  (p.  64),  "the  distinction  between 
Concepts  and  Marks  is  not  absolute,  but  relative;  they 
may  be  used  interchangeably."  That  a  Concept  or  Com- 
mon Name  is  sometimes  used  only  as  a  Mark,  or  with  no 
conscious  reference  at  the  moment  to  its  denotation,  is 
surely  no  proof  that  it  is  always  so  used,  or  even  that  the 
denotative  meaning,  or  Extension,  is  not  potentially  present 
in  this  very  case,  so  that  it  may  be  revived,  if  need  be, 
and  an  inference  founded  upon  it.  Because  words  are 
sometimes  used  symbolically,  or  without  spreading  out  in 
Thought  all  their  signification,  it  does  not  follow  that  they 
are  always  so  used,  or  that  such  use  of  them  may  not  be 
checked,  and  kept  from  falling  into  error,  by  occasionally 
bringing  up  into  consciousness  what  they  always  potentially 
signify  in  Thought.  It  follows,  then,  that  although  a  Judg- 
ment, as  actually  iliought,  may  not  be  a  truth  of  classification, 
and  therefore  that  the  Copula  may  not  be  equivalent  to  the 
mathematical  sign  of  equality,  yet  it  may  always  be  reduced 
to  the  form  of  such  a  truth,  and  then  this  mathematical 
sign  fully  expresses  its  proper  form;  and  in  reasoning, 
such  a  reduction  is  generally  necessary.  Though  it  is  not 
true  that  apple  =  red,  it  is  true  that  apples  =  some  red 
object*  ;  or,  as  it  is  more  commonly  expressed  by  Conver- 
sion, some  red  objects  are  apples. 


112  THE  DOCTRINE  OF  JUDGMENTS. 

1.     The  Predicables  and  the  Categories. 

In  his  analysis  of  Judgments,  Aristotle  was  led  tcv  con- 
sider how  many  kinds  of  Predicates  there  are,  when 
viewed  relatively  to  their  Subjects ;  —  in  other  words,  tc 
determine  the  Second  Intentions  of  Predicates  considered 
in  relation  to  Subjects.  Thus  was  formed  his  celebrated 
doctrine  of  the  Predicables,  —  a  doctrine  which  was  con- 
siderably modified,  but  not  improved,  by  his  followers, 
Porphyry  and  the  Schoolmen.  According  to  Aristotle, 
every  Judgment  affirms  or  denies  one  of  four  relations  of 
a  Predicate  to  its  Subject.  It  expresses  either,  —  1.  xhe 
Genus,  i.  e.  the  class  under  which  it  is  included,  as  when 
we  say,  man  is  an  animal;  or,  2.  the  Definition,  which, 
as  we  have  seen,  is  the  Genus  and  the  Specific  Difference 
taken  together,  and  may  be  reduced  to  an  enumeration 
of  all  the  essential  Marks  of  the  Subject,  as,  a  Carnivoty 
is  a  flesh-eating  Mammal;  or,  3.  a  Property,  that  is,  some 
peculiar  attribute  of  the  Subject,  belonging  to  it  univer- 
sally, belonging  to  nothing  else,  and  yet  not  regarded  as 
essential  to  it,  for  we  could  conceive  of  the  thing  without 
it,  —  as  polarity  is  a  Property  (proprium)  of  the  magne\ 
and  risibility  of  man;  or,  4.  an  Accident,  which  is  air 
attribute  that  happens  to  belong  to  the  Subject,  but,  a9 
unessential,  is  separable  from  it,  as  man  is  learned. 

Two  of  these  Predicables,  namely,  the  Definition  and 
the  Property,  are  convertible  with  the  Subject,  or  may 
change  places  with  it ;  and  of  these  two,  the  former  ex- 
presses the  whole  Essence  (all  the  essential  qualities),  while, 
the  latter,  strictly  speaking,  is  no  part  of  the  Essence ;  for 
we  can  conceive  of  man  as  not  having  the  attribute  of 
risibility,  but  we  cannot  conceive  of  him  as  deprived  of 
rationality.  So,  the  magnet  can  be  conceived  of  without 
polarity,  as  its  magnetic  or  attractive  power  was  known 
long  before  its  property  of  pointing  to  the  north  was  dis- 


THE  PREDICABLES  AND  THE  CATEGORIES.      113 

covered ;  but  its  magnetic  or  attractive  quality  is  essential 
to  our  conception  of  it.  Of  the  two  other  Predicables, 
Genus  and  Accident,  neither  is  convertible  with  the  Sub- 
ject ;  and,  again,  the  former  expresses  a  part  of  the  Essence, 
and  the  latter  does  not.  Thus  we  have  the  following 
scheme  of  the  Predicables:  — 

Definition  expressing  the  whole  Essence  )  convertible 

Property  expressing  no  part  of  the  Essence  j  with  the  Subject. 

Genus  expressing  a  part  of  the  Essence  >  inconvertible 

Accident  expressing  no  part  of  the  Essence  j  with  the  Subject. 

Porphyry  and  the  Schoolmen  modified  this  analysis,  but 
did  not  improve  it,  in  their  attempt  to  make  it  conform 
to  their  philosophical  doctrine  of  Realism.  The  Realists 
maintained,  that  Universals  or  Species  are  not  mere  classes 
of  things  arbitrarily  formed  by  the  mind,  but  are  real  exist- 
ences, with  perfectly  well-defined  limits,  existing  in  things, 
and  yet  independently  of  them  and  of  our  conceptions 
of  them.  Each  Universal  is  the  common  and  essential 
element  —  the  Essence  —  of  all  the  individual  things  which 
are  included  under  it  and  denoted  by  its  Name.  What- 
ever other  attributes  these  individuals  possess  do  not  belong 
to  their  Essence,  but  are  considered  as  their  Properties 
or  Accidents.  According  to  this  view,  Species  has  a  de- 
terminate and  fixed  meaning,  corresponding  very  nearly 
to  what  we  have  termed  the  Infima  Species;  it  was 
absolutely  the  lowest  class  to  which  anything  can  be  re- 
ferred, and  not  merely  the  lowest  relatively,  as  we  have 
defined  it.  Every  Specific  Difference,  moreover,  signifies 
absolutely  the  attribute  whereby  a  given  Species  is  dis-. 
tinguished  from  every  other  Species  of  the  same  Genus. 
Both  Species  and  Genus  are  thus  supposed  to  be  absolutely 
determined,  following  the  patterns  or  archetypes  of  them 
which  exist  in  the  Divine  Mind,  and  which  presided  over 
their  creation,  instead  of  being  mere  creatures  of  our 
Thought,  and  springing  from  arbitrary  classifications,  ac- 


114  THE  DOCTRINE  OF  JUDGMENTS. 

cording  to  which  the  same  individual  may  be  referred  to 
any  one  of  several  different  Species,  and  again  the  same 
Species  to  one  Genus  or  another,  according  as  it  suits  our 
purpose.  The  Realists  maintained  that  the  hierarchy  of 
classification  is  not  fluctuating  and  arbitrary,  formed  by 
man  for  his  own  convenience,  and  therefore  always  chang- 
ing to  suit  his  ever- varying  purposes ;  but  they  held  that 
it  resulted  from  the  real  nature  of  things,  as  determined 
by  the  Creator,  and  therefore  is  a  perfect  and  immutable 
copy  of  the  Divine  Thought.  To  adopt  Mr.  Mill's  lan- 
guage, "  they  did  not  admit  every  class  which  could  be 
divided  into  other  classes  to  be  a  Genus,  or  every  class 
which  could  be  included  in  a  larger  class  to  be  a  Species. 
Animal  was  by  them  considered  a  Genus;  and  man  and 
brute,  co-ordinate  Species  under  that  Genus  :  biped  would 
not  have  been  admitted  to  be  a  Genus  with  reference  to 
man,  but  a  proprium  or  accidens  only.  It  was  requisite, 
according  to  their  theory,  that  Genus  and  Species  should 
be  of  the  Essence  of  the  Subject.  Animal  was  of  the 
Essence  of  man;  biped  was  not.  And  in  every  classifi- 
cation, they  considered  some  one  class  as  the  lowest  or 
Infima  Species ;  man,  for  instance,  was  a  lowest  Species. 
Any  other  divisions  into  which  the  class  might  be  capa- 
ble of  being  further  broken  down,  as  man  into  white,  black, 
and  red  man,  or  into  priest  and  layman,  they  did  not 
admit  to  be  Species."  They  wrongly  assumed,  —  1.  that 
the  Divine  Mind  classifies  at  all  (see  p.  15) ;  2.  that  it 
would  be  possible  for  man  to  follow  the  thought  of  the 
Creator  so  far  as  to  copy  without  error  such  classification, 
even  if  it  existed ;  3.  that  there  is  no  occasion,  even  for 
purposes  of  human  science  and  convenience,  to  distribute 
the  same  individual  things  into  different  systems  of  clas- 
sification, assuming  various  Grounds  of  Division,  according 
to  the  special  ends  in  view. 

Adopting  the  Realist  hypothesis,  the  Schoolmen  distin- 


THE  PREDICABLES  AND   THE   CATEGORIES.  115 

guished  these  five  Predicables,  —  Genus,  Species,  Differ- 
ence, Property,  and  Accident.  Comparing  this  list  with 
that  of  Aristotle,  we  perceive  that  Definition  is  omitted, 
—  being  resolved  into  its  two  elements,  Genus  and  Specific 
Difference,  both  of  which  are  admitted  into  this  scheme,  — 
and  that  Species  also  is  added.  The  Species  here  intended 
is  the  Infima  Species,  or  proximate  class,  and  is  usually  de- 
fined as  being  the  whole  Essence  of  the  individuals  of 
which  it  is  predicated.  Difference  is  also  taken  abso- 
lutely, being  regarded  as  predicable  of  this  class  and  of 
none  other,  —  that  is,  as  serving  to  distinguish  this  Species, 
not  merely  from  the  other  Species  in  the  same  Genus,  but 
from  all  others  whatever.  Aristotle  omitted  Difference 
from  his  list,  because,  as  he  says,  it  is  "  of  the  nature  of 
Genus,"  or,  as  we  should  say,  it  is  interchangeable  with 
Genus.  In  truth,  each  of  the  two  elements  of  a  Definition 
is  a  Genus ;  they  are  two  communicant  or  overlapping 
Genera.  But  it  is  more  convenient  to  regard  one  as  de- 
termined, and  the  other  as  determining,  —  that  is,  one  a& 
Genus  and  the  other  as  Difference.  Thus,  man  is  a  ra- 
tional animal;  here  are  two  Genera,  rational  beings  and 
animal  beings,  which  partially  include,  and  partially  ex- 
clude, each  other.  As  there  are  some  rational  beings 
which  are  not  animal  (angels,  for  instance),  so  there  are- 
some  animals  (brutes)  which  are  not  rational ;  but  man  is 
both  animal  and  rational,  —  that  is,  he  is  the  common  part 
of  the  two  overlapping  Genera.  He  is,  therefore,  a  rational 
animal  being,  or,  what  is  precisely  the  same  thing,  he  is  an 
animalized  rational  being.  In  the  former  case,  animal  is  the 
Genus  and  rational  is  the  Specific  Difference  ;  in  the  latter 
case,  this  is  reversed,  rational 
oeing  the  Genus  and  animal 
Jie  Difference.  Thus :  — 
Let  A  sa  animal ; 
B  =  rational ; 
then,  C  =  rational  animal. 


116  THE  DOCTRINE  OF  JUDGMENTS. 

Aristotle  evidently  perceived,  what  his  followers  did  not, 
that  there  is  no  real  distinction  between  Genus  and  Differ- 
ence ;  that  both  of  them  are,  in  truth,  Genera  ;  and  hence 
that  Difference,  being  of  the  nature  of  Genus,  cannot  be 
admitted  into  the  list  of  distinct  Predicables. 

Having  ascertained  the  Second  Intentions  of  Predicates, 
which  are  the  Predicables,  Aristotle  attempted  to  carry  the 
analysis  of  Judgments  one  step  farther,  by  determining  their 
First  Intentions,  and  was  thus  led  to  form  his  celebrated 
list  of  the  ten  Categories  or  Predicaments.  In  other  words, 
having  determined  how  many  sorts  of  Predicates  there  are 
in  relation  to  their  Subjects,  he  next  inquired  how  many 
and  what  particular  things  may  be  predicated  of  any  Sub- 
ject. Considering  eveiy  Judgment  as  the  answer  to  a 
question,  he  sought  to  ascertain  how  many  and  what  dif- 
ferent questions  may  be  asked  concerning  a  Subject,  —  what 
are  the  several  determinations  of  which  it  is  capable.  The 
inquiry  evidently  concerns  the  Matter,  and  not  the  Form, 
of  Thought,  and  therefore  does  not  properly  fall  within  the 
province  of  Logic,  which  is  exclusively  occupied  with  Sec- 
ond Intentions.  But  the  Categories  may  be  regarded  as  a 
curiosity  in  the  history  of  the  science,  and  as  a  monument 
of  the  genius  of  its  founder  for  abstract  thought  and  com- 
prehensive generalization.  Great  ingenuity  has  been 
wasted  upon  the  discussion  of  them  by  his  followers.  For 
many  centuries,  during  which  the  boundaries  of  the  science 
were  not  so  strictly  defined  as  they  now  are,  the  doctrine 
of  the  Categories  occupied  a  prominent  place  in  every 
treatise  upon  Logic.  A  very  brief  explanation  of  it  will 
answer  our  present  wants. 

The  Greek  verb  from  which  category  is  derived  properly 
signifies  to  accuse,  or  to  affirm  something  of  any  one,  and 
hence,  to  predicate.  But  the  noun  has  been  diverted  by 
logicians  from  signifying  affirmation  or  predication,  and 
applied  to  a  list  or  class  of  things  of  the  same  kind  which 
may  be  predicated  of  any  Subject.     Aristotle  affirms  that 


THE  PREDICABLEo  AND  THE  CATEGORIES.      117 

there  are  ten  Categories,  or  classes  of  things  that  may  be  so 
predicated,  —  namely,  1.  Substance;  2.  Quantity;  3.  Qual- 
ity ;  4.  Relation  ;  5.  Place  ;  6.  Time  ;  7.  Posture  ;  8.  Pos- 
session ;  9.  Action ;  10.  Passion.  According  to  a  fashion 
very  common  among  the  Scholastic  logicians,  of  manufac- 
turing Latin  verses  as  aids  to  the  memory  in  retaining  the 
technicalities  of  the  science,  the  several  Categories  are  in- 
dicated in  the  two  following  lines,  though  in  a  somewhat 
different  order  from  that  given  above,  as  shown  by  the 
numerals  prefixed. 

12         3  4  9  10 

Arbor  sex  servos  fervore  refrigcrat  ustos  ; 

5        6       7  8 

Ruri  eras  stabo,  nee  tunicatus  ero. 

The  four  Predicables,  argues  Aristotle,  —  "  the  Accident, 
the  Genus,  the  Property,  and  the  Definition,  —  will  always 
be  in  one  of  these  Categories  [or  classes]  ;  since,  through 
these,  all  propositions  signify  either  what  the  Subject  is,  or 
how  much  it  is,  or  what  sort  of  a  thing  it  is,  or  some  one  of 
the  other  Categories";  as,  what  relation  it  bears  to  some 
other  thing,  or  its  place,  its  time,  its  posture,  what  it  has, 
or  does,  or  suffers.  Adopting  Aristotle's  own  examples  of 
predication  under  each  of  these  classes,  we  may,  for  in- 
stance, affirm  of  anything,  —  1.  under  the  Category  of 
Substance,  that  it  is  a  man,  a  horse,  or  the  like  ;  2.  under 
that  of  Quantity,  that  it  is  two  cubits  long,  three  cubits, 
&c. ;  3.  under  that  of  Quality,  that  it  is  white,  grammat- 
ical, &c. ;  4.  under  that  of  Relation,  that  it  is  double,  half 
as  large,  greater,  &c.  ;  5.  under  that  of  Place,  in  the 
Lyceum,  in  the  Forum,  &c. ;  6.  under  that  of  Time,  yes- 
terday, last  year,  &c. ;  7.  under  Posture,  standing,  seated, 
&c. ;  *  8.  under  Possession,*  having  shoes  or  armor,  &c. ; 

*  Many  writers  have  interpreted  Aristotle's  seventh  Category,  Kciatiat,  as 
iSituation.  But,  as  Situation  is  identical  with  Place,  this  interpretation  makes 
the  seventh  redundant  and  unnecessary.  Besides,  the  examples  here  selected 
prove  that  Aristotle  here  understands  Kficrdai  to  signify  Posture. 


118  THE  DOCTRINE  OF  JUDGMENTS. 

9.  under  Action,  it  cuts,  burns,  &c. ;  10.  under  Passion, 
it  is  cut,  is  burned,  &c. 

The  purpose  of  Aristotle  in  framing  his  scheme  of  the 
Categories,  and  the  nature  of  the  Categories  themselves, 
have  been  very  differently  understood  by  different  writers, 
who,  in  commenting  upon  them,  seem  to  have  had  much 
more  reference  to  their  own  systems  of  metaphysical  phi- 
losophy than  to  a  fair  interpretation  of  the  text  of  fcieir 
author.  Thus,  Kant  assumes  that  Aristotle's  intention  was 
to  form  a  complete  list  of  the  a  'priori  conceptions  of  the 
intellect,  or  of  the  forms  which  the  mind  imposes  upon 
things  by  its  own  mode  of  thinking  them.  Under  this  in- 
terpretation, he  asserts  very  truly,  that  the  analysis  is  not 
formed  upon  any  one  principle  ;  that  the  enumeration  is 
incomplete  ;  that  empirical  notions  are  intruded  among  tho 
pure,  and  derivative  among  those  which  are  original. 

Mr.  Mill  supposes  that  the  Categories  are  "  an  enumera- 
tion of  all  things  capable  of  being  named,  —  an  enumera- 
tion by  the  summa  genera;  that  is,  the  most  extensive 
classes  into  which  things  could  be  distributed ;  which, 
therefore,  were  so  many  highest  Predicates,  one  or  other 
of  which  was  supposed  capable  of  being  affirmed  with 
truth  of  every  namable  thing  whatsoever."  Taken  in 
this  light,  he  finds,  of  course,  that  the  list  is  both  redun- 
dant and  defective  ;  that  Relation  includes  Action,  Passion, 
and  several  others ;  and  that  u  mental  states,"  which,  in 
Mr.  Mill's  opinion,  are  neither  substances  nor  attributes, 
are  omitted  entirely. 

Sir  William  Hamilton's  interpretation  of  the  Categories 
agrees  very  nearly  with  that  of  Mr.  Mill.  He  finds  that 
they  are  an  enumeration  of  the  highest  genera  of  Being 
or  Existence,  —  that  is,  of  all  things  whatsoever ;  and, 
under  this  view,  justly  objects  that  Being  ought  first  to  be 
divided  by  dichotomy,  into  absolute  and  relative  Being, 
the  first  of  which  coincides  with  Aristotle's  first  Category, 


THE  PREDICABLES  AND  THE  CATEGORIES.      119 

that  of  Substance,  while  the  second  includes  the  other 
nine ;  and  that  the  last  six  may  all  be  reduced  to  the 
fourth,  that  of  Relation. 

Trendelenburg,  who  is  followed  by  Mr.  Mansel,  main- 
tains that  the  Categories  are,  to  adopt  the  language  of  the 
latter,  "  an  enumeration  of  the  different  modes  of  naming 
things,  classified  primarily  according  to  the  grammatical 
distinctions  of  speech,  and  gained,  not  from  the  observation 
of  objects,  but  from  the  analysis  of  assertions."  This 
doctrine  seems  to  be  correct ;  but  it  is  obviously  irrelevant, 
for  it  explains  only  the  genesis,  not  the  nature,  of  the 
Categories.  To  show  the  source  of  the  classification,  or 
how  Aristotle  was  led  to  make  ft,  is  very  different  from 
explaining  the  nature  of  the  things  classified,  and  the  real 
distinctions  between  the  several  classes. 

And  the  ground  for  the  other  criticisms  falls  away  when 
it  is  considered,  that  the  distinction  between  the  Form  and 
the  Matter  of  Thought  —  that  is,  between  Logic  and 
Metaphysics  —  is  but  very  imperfectly  preserved  by  Aris- 
totle. But  although  much  of  what  properly  belongs  to 
Metaphysics  is  intruded  into  his  treatises  upon  Logic,  and 
vice  versa,  it  is  never  considered  there  primarily  in  its 
metaphysical  nature,  but  only  in  its  logical  relations.  The 
doctrine  of  the  Categories,  as  conceived  by  him,  is  not 
an  attempt  to  enumerate  the  highest  classes  into  which 
things  in  general  can  be  distributed;  for  this  would  be  a 
purely  metaphysical  speculation,  and,  as  such,  open  to 
criticism  on  metaphysical  grounds.  But  it  is  a  classification 
of  things  in  so  far  only  as  these  things  are  predicates,  — 
that  is,  of  things  considered  merely  in  one  of  their  logical 
aspects.  To  such  a  classification,  metaphysical  objections, 
like  those  of  Kant,  Mill,  and  Hamilton,  are  evidently 
irrelevant.  For  instance  :  —  metaphysically,  Place  is  in- 
cluded under  Relation,  for  it  is  the  relation  of  a  subject 
to  a  fixed  point  in  space.     But,  logically,  these  two  Cate- 


120  THE  DOCTKINE   OF  JUDGMENTS. 

gories  are  distinct ,  for  it  is  one  thing  to  assign  a  Subject 
to  a  fixed  point  in  space ;  a  second,  to  assign  its  relation  to 
another  thing  in  quantity  or  quality;  and  a  third  and  fourth, 
to  assign  its  quantity  and  quality  absolutely.  Aristotle's 
scheme  or  general  conception  of  the  Categories  may  be 
censured,  as  depending  on  a  mixture  of  two  incongruous 
aspects  of  Thought,  the  logical  and  the  metaphysical ;  but 
for  all  that  appears,  it  is  as  well  executed  as  such  a  hybrid 
scheme  can  be. 

%.    The  Quantity,  Quality,  and  Relation  of  Judg- 
ments,  ACCORDING   TO  THE   ARISTOTELIC   DOCTRINE. 

The  question  now  arises,  how  many  things  can  be  de- 
termined about  a  Judgment  considered  merely  as  such,  - 
that  is,  by  considering  its  mere  Form,  without  reference 
to  the  Matter  of  the  Concepts  which  are  its  Terms.  In 
the  first  place,  we  may  inquire  concerning  the  number 
of  objects  about  which  we  judge,  and  thus  determine  the 
Quantity,  or  Extension,  of  the  Judgment.  Secondly,  we 
may  ask  what  sort  of  a  Judgment  we  form  respecting  the 
two  Terms,  —  that  is,  whether  we  affirm  a  relation  of 
agreement  or  of  disagreement  between  them ;  we  thus 
ascertain  the  Quality  of  the  Judgment,  or  whether  it  is 
affirmative  or  negative.  Thirdly,  we  may  inquire  respect- 
ing the  different  modes  in  which  a  relation  of  agreement 
or  difference  between  the  two  terms  may  be  affirmed,  and 
thus  determine  what  is  called  the  Relation  of  a  Judgment. 
In  this  manner  are  answered  the  three  questions  which 
may  be  asked  concerning  any  Judgment  or  Proposition 
whatsoever,  —  Quanta  t  qualis  f  quce  ? 

A  fourth  question  has  generally  been  asked  by  logicians, 
as  to  the  degree  of  certainty  with  which  a  Judgment  is 
affirmed.  This  was  called  the  Modality  of  the  Judgment, 
being  the  mode  or  measure  in  which  we  hold  it  to  be  true. 


THEIR   QUANTITY,   QUALITY,   AND  RELATION.  121 

Several  degrees  of  it  were  usually  distinguished,  according 
to  the  following  formulas:  — 
Judgments  are  either 

Pure  A  is  B.        %  Assertorical. 

(  A  may  be  B.  Contingent  or  Problematic. 

,,   ,  .  ]  A  must  be  B.  Necessary.    > 

ModaI  \  A  cannot  be  B.  Impossible.  (  Demonstrative. 

[  A  can  be  B.  Possible. 

But  the  whole  doctrine  of  Modality  is  now  rightfully 
banished  from  Pure  Logic,  as  it  evidently  belongs  not  to 
the  Form,  but  to  the  Matter,  of  Thought.  Any  number 
of  Modal  Propositions  may  be  framed,  all  of  which  would 
have  as  good  a  claim  to  consideration  as  those  just  specified 
Thus,  A  is  rightfully  B,  A  is  justly  B,  A  is  maliciously 
B,  are  as  good  Modals  as  A  is  possibly  B,  or  A  is  certainly 
B.  In  truth,  since  the  Copula  in  Logic  is  only  a  sign 
of  equality,  or  the  present  tense  of  the  verb  to  be,  the 
qualifying  word  must  be  logically  regarded  as  a  portion 
of  the  Predicate;  thus,  A  is  a  possible,  or  a  necessary  B. 
Hence  it  is  manifest  that  the  signs  of  Modality  belong 
to  the  Matter  of  the  Thought,  with  which  here  we  have 
no  concern. 

In  respect  to  Quantity,  according  to  the  Aristotelic 
logicians,  Judgments  are  either  Universal  or  Particular. 
A  Universal  Judgment  is  one  in  which  the  Predicate  is 
affirmed  of  the  whole  Subject  taken  distributively.  Thus, 
All  men  (i.  e.  each  and  every  man)  are  mortal ;  No  quad- 
ruped (i.  e.  not  any  one  out  of  all  quadrupeds)  is  rational ; 
are  Universal  Judgments. 

A  Particular  Judgment  is  one  in  which  the  Predicate 
is  affirmed  only  of  a  part — an  indefinite  part  —  of  the 
Subject.  For  example:  Some  men  (i.  e.  some  at  least, 
some  —  I  know  not  how  many)  are  learned;  Some  trees  are 
not  deciduous. 

On  the  other  hand,  all  taken  collectively  (as,  All  the 
Greeks  —  i.  e.  the  Greek  nation  —  conquered  the  Persians), 


122  THE  DOCTRINE   OF   JUDGMENTS. 

is  the  sign  of  a  Singular  or  Individual  Judgment,  in  which 
a  Predicate  is  affirmed  of  one  thing,  or  of  a  class  of  things 
taken  as  one  whole.  But  as  here  also  the  Predicate  is 
affirmed  of  the  whole  Subject,  Singular  Judgments,  for  all 
logical  purposes,  are  considered  as  Universals. 

In  like  manner,  some  certain  —  some,  a  definite  part  — 
embracing  these  very  cases  which  I  am  thinking  of  and 
no  other  —  is  the  sign,  not  of  a  Particular,  but  of  a 
Singular  Judgment,  and  is  therefore  properly  ranked  with 
Universals. 

"  Individual  names,"  says  Mr.  Mansel,  "  are  distin- 
guished as  individua  signata,  expressed  by  a  proper  name, 
as  Socrates;  individua  demonstrativa,  by  a  demonstrative 
pronoun,  hie  homo ;  individua  vaga,  by  an  indefinite  pro- 
noun, aliquis  homo,  quidam  homo."  But  he  properly  ob- 
jects that  this  last  class,  the  indefinites,  ought  to  be  consid- 
ered as  Particulars  rather  than  as  Singulars.  "  If  we  say 
quidam  conscionatur,  quidam  legit,  there  is  no  evidence  that 
the  same  person  is  spoken  of  in  the  two  propositions ;  while 
Socrates,  except  by  a  mere  quibble,  will  always  designate 
the  same  person.  There  may,  indeed,  be  two  persons  of 
the  same  name  ;  but,  in  this  case,  the  name  fails  to  accom- 
plish the  intended  distinction,  and  we  must  specify,  —  Soc- 
rates the  son  of  Sophroniscus." 

The  logicians  formerly  distinguished  another  class  of 
Judgments  as  Indefinite,  meaning  those  in  which  the  Sub- 
ject, having  no  sign  or  predesignation  of  Quantity  affixed 
to  it,  is  not  expressly  declared  to  be  either  Universal,  Sin- 
gular, or  Particular.  Thus,  Elephants  are  sagacious  ani- 
mals ;  —  Learned  men  are  to  he  found  at  Oxford.  But  this 
omission  of  the  predesignation  of  Quantity  is  merely  an 
accident  of  expression,  and  therefore  belongs  only  to  Propo- 
sitions, and  not  to  Judgments,  which  are  always  thought  as 
having  some  one  of  the  three  specified  kinds  of  Quantity. 
According  to  the  Postulate  of  Logic,  which  requires  us  to 


THEIR  QUANTITY,   QUALITY,  AND  RELATION.  123 

state  explicitly  all  that  is  implicitly  thought,  the  two  exam- 
ples just  given  are  logically  stated  thus  :  All  elephants  are 
sagacious  ; — Some  learned  men  are  found  at  Oxford. 

An  improved  classification  or  nomenclature  of  Judgments 
in  respect  to  Quantity  is  proposed  by  Sir  William  Hamilton. 
Since  both  Universals  and  Singulars  have  a  determinate  or 
known  Quantity,  —  namely,  the  whole  either  of  a  class  or 
of  a  unit,  —  he  would  call  them  Definite  Judgments ;  while 
Particulars,  expressing  an  indeterminate  or  unknown  part 
of  a  whole,  should  be  called  Indefinite.  But  as  confusion 
might  arise  from  abandoning  technical  terms  which  have 
been  so  long  in  use,  we  shall  continue  to  distinguish  Judg- 
ments in  respect  to  Quantity  as  either  Universal  or  Partic- 
ular, Singular  being  ranked  with  the  former,  and  the  latter 
expressing  an  indefinite  part. 

In  respect  to  Quality,  Judgments  are  distinguished  as 
either  Affirmative  or  Negative,  according  as  they  affirm  a 
union  or  a  disjunction  of  their  two  Terms.  In  every  real 
Negative  Judgment,  the  negative  particle,  wherever  in 
the  sentence  it  may  appear,  belongs  only  to  the  Copula ; 
since  the  question  always  is,  whether  a  union  of  the 
Subject  and  Predicate  is,  or  is  not,  affirmed.  Hence  the 
presence  of  a  negative  particle  in  the  proposition  is  not  a 
sure  sign  that  it  is  a  Negative  Judgment,  for  this  particle 
may  belong  in  thought  to  one  of  the  two  Terms.     Thus, 

"  Nil  admirari  prope  res  est  una,  Numici  "  ;  — 
"  Not  to  admire  is  all  the  art  I  know  "  ;  — 
"  ^Eneas  potuit  —  non  vincere  Turnum  "  ;  — 

are  Affirmative  Judgments.  This,  also,  is  an  affirma- 
tion :  — 

"  Una  salus  victis  —  nullara  sperare  salutem." 

"  The  only  chance  of  preservation  for  the  vanquished  is,  not  to  hope  for 
preservation." 

Hence,  by  an  easy  artifice,  a  Negative  Judgment  may 
be  changed,  in  Form,  to  an  Affirmative  one  of  equivalent 


124  THE  DOCTRINE  OF  JUDGMENTS. 

meaning,  by  taking  off  the  negation  from  the  Copula,  and 
affixing  it  to  the  Predicate.  Thus,  X  is  not  Y,  is  the 
same  as,  X  is  not-Y ;  for  if  the  universe  is  divided  into 
only  two  parts,  Y  and  not-Y,  the  exclusion  of  X  from  one 
of  these  parts  is  necessarily  an  inclusion  of  it  in  the  other. 
And  as  two  negatives  cancel  each  other,  an  Affirmative 
may  be  made  to  take  the  Form  of  a  Negative  Judgment, 
by  negativing  both  the  Copula  and  the  Predicate.  X  is 
Y,  may  be  changed  into,  X  is  not  not-Y.  "  The  soul  is 
indivisible,"  is  equivalent  to  "  The  soul  is  not  divisible  " ; 
and  "  All  the  righteous  are  happy,"  is  the  same  as  "  Not 
any  of  the  righteous  are  unhappy."  We  shall  soon  see 
what  use  can  be  made  of  this  artifice  in  the  doctrine  of 
Immediate  Inference. 

By  combining  the  Quantity  and  Quality,  as  there  are 
two  kinds  of  each,  we  have  four  distinct  forms  of  Judg- 
ments, which  are  designated  by  the  four  vowels  A,  E, 
I,  O.  To  aid  the  memory,  these  distinctions  have  been 
expressed  in  this  Latin  distich:  — 

Asserit  A,  negat  E,  sed  universaliter  ambae, 
Asserit  I,  negat  O,  scd  particulariter  arabo. 

These  lines  have  been  thus  translated  into  English  dog- 
gerel :  — 

A,  it  affirms  of  this,  these,  aU, 

Whilst  E  denies  of  any ; 
I,  it  affirms,  whilst  O  denies, 

Of  some  (or  few  or  many).* 

Examples  of  these  Propositional  Forms,  as  they  art 
called,  are  given  in  the  following  table :  — 

Symbols.  Examples.  Quality.  Quantity. 

A.    All  animals  are  sentient.       Affirmative.  ?  tt  •         i 


E.    No  plant  is  sentient.  Negative.       £ 

I.      Some  men  are  honest.  Affirmati 

O-    Some  trees  are  not  maples.     Negative 


I.      Some  men  are  honest.  Affirmative.  }  part;PUiar 


*  It  is  suggested  by  Hamilton,  with  great  plausibility,  that  these  foui 
letters  were  selected  because  A  and  I  are  the  first  two  vowels  in  affirmo,  E 
and  O  the  two  vowels  in  nego. 


THEIK   QUANTITY,   QUALITY,   AND   RELATION.  125 

Observe,  however,  that  though  the  predesignation  all 
is  the  sign  of  A,  a  Universal  Affirmative,  not  all  is  not 
the  sign  of  E,  a  Universal  Negative,  but  is  always  Par- 
ticular, and  leaves  the  Quality  ambiguous,  as  it  may  be 
either  Affirmative  or  Negative.  Not  all  denies  univer- 
sality, and  is  a  direct  assertion  that  some  are  not,  and  an 
implied  assertion  that  some  are.  Thus,  Not  all  is  gold  that 
glitters,  asserts  directly  that  some  glittering  things  are  not 
gold,  and,  by  implication,  that  some  glittering  things  are 
gold.  "Not  every  one  who  says  unto  me,  Lord!  Lord! 
shall  enter  into  the  kingdom  of  Heaven " ;  —  i.  e.  some 
who  say  this  shall  not  enter. 

The  predesignation  some  is  likewise  ambiguous.  It  may 
mean  some  at  least,  —  i.  e.  some,  perhaps  all;  or  it  may 
mean  some  at  most,  —  i.  e.  some,  not  all.  Thus,  a  chemist 
might  say,  Some  metals  are  dissolved  by  acids,  meaning 
"  Perhaps  all  metals  are  thus  soluble,  but  at  any  rate,  some 
are."  On  the  other  hand,  he  may  say,  Some  metals  are 
malleable,  meaning,  some — excluding  all,  for  he  knows  that 
some  metals  are  not  malleable.  In  a  Negative  Judgment, 
if  we  consider  some  to  mean  perhaps  all,  it  is  evident  that 
"  Some  X  is  not  Y  "  may  be  construed  "  Perhaps  no  X  is 
Y  "  ;  but  if  some  signifies  not  all,  then  some  is  not  excludes, 
or  is  inconsistent  with,  none  —  not  one.  The  wholly  indefi- 
nite meaning,  some,  perhaps  all,  is  the  one  generally  re- 
ceived in  Logic ;  the  other  meaning  is  called  by  Sir  W. 
Hamilton  semi-definite,  because,  by  excluding  all,  it  is  so  far 
definite.  Though  this  latter  meaning  has  been  generally 
neglected  by  logicians,  it  leads,  as  we  shall  see  hereafter, 
to  some  important  additional  inferences,  and  modifies,  to  a 
considerable  extent,  the  old  doctrines  concerning  Opposition. 

Hitherto  we  have  considered  the  Quantity  of  the  Judg- 
ment only,  and  we  have  now  to  consider  the  Quantity  of 
the  two  Terms  as  affected  by  the  Judgment  in  which  they 
stand.     A  Term  is  said  to  be  distributed  when  it  is  taken 


126  THE  DOCTRINE  OF  JUDGMENTS. 

distributively,  or  in  the  whole  of  its  Extension,  —  that  is, 
when  it  is  affected,  or  should  be  affected,  by  the  predesig- 
nations  all,  each,  none,  &c. ;  it  is  not  distributed  when  it  is 
taken  only  in  an  indefinite  part  of  its  Extension,  —  as 
usually  signified  by  the  predesignations  some,  not  all,  &c. 
The  received  or  Aristotelic  doctrine  upon  this  matter  is, 
that  the  distribution  of  the  Subject  depends  upon  the  Quan- 
tity of  the  Judgment,  thus ;  —  in  Universal  Judgments,  the 
Subject  is  distributed,  but  in  Particular  Judgments,  it  is 
not  distributed.  No  unjust  action  is  expedient ;  —  this  is  a 
Universal  Proposition,  and  its  Subject  is  evidently  dis- 
tributed, as  the  meaning  is,  not  any  one  out  of  all  unjust 
actions  is  expedient.  But  in  the  Particular  Proposition, 
Some  men  are  learned,  it  is  obvious  that  the  Subject,  men, 
is  not  distributed. 

On  the  other  hand,  the  distribution  of  the  Predicate 
depends  upon  the  Quality  of  the  Judgment,  thus ;  —  in 
Negative  Judgments,  the  Predicate  is  distributed,  but  in 
Affirmatives,  it  is  not  distributed.  This  rule  is  evidently 
founded  upon  the  doctrine  that  all  predication  is  classifica- 
tion ;  and  consequently,  that  when  we  affirm,  we  thereby 
include  the  Subject  in  the  class  denoted  by  the  Predicate, 
not  meaning  that  the  Subject  constitutes  the  whole  of  that 
class,  but  only  a  part  of  it ;  and  that,  when  we  deny,  we 
thereby  exclude  the  Subject  wholly,  or  from  any  part  of 
the  class.  Thus,  when  we  say,  "  Men  are  animals,"  we 
mean,  "  Men  are  some  animals,"  since  it  is  not  true  that 
all  animals  are  men.  On  the  other  hand,  when  we  say, 
"No  man  is  immortal,"  we  mean  to  exclude  man  from 
every  part  of  the  class  of  "  immortal  beings,"  so  that  no 
immortal  whatever  can  be  human.  And  even  in  the  case 
of  Particular  Negatives,  as,  "  Some  Frenchmen  are  not 
Parisians,"  we  still  mean  absolute  or  total  exclusion, — 
that  not  any  Parisian  whatever  is  one  of  the  "Some 
Frenchmen  "  —  say,  inhabitants  of  Lyons  —  whom  we  were 
speaking  of. 


THEIR   QUANTITY,   QUALITY,   AND  RELATION.  127 

According  to  this  doctrine,  the  four  fundamental  Judg- 
ments, if  the  statements  are  intended  to  convey  the  whole 
Thought  which  is  implied  in  them,  must  be  thus  ex- 
pressed :  — 

A.'  All  X  are  some  Y.  All  animals  are  some  sentient 
beings. 

E.    No  X  is  any  Y.     No  plant  is  any  sentient  being. 

I.  Some  X  are  some  Y.  Some  men  are  some  honest 
persons. 

O.  Some  X  are  not  any  Y.  Some  trees  are  not  any  ma- 
ples. 

Hence  the  rule  for  the  distribution  of  the  two  Terms 
in  a  Judgment  may  be  thus  briefly  expressed :  —  In  A, 
only  the  Subject  is  distributed ;  in  O,  only  the  Predicate  ; 
in  I,  neither ;  in  E,  both. 

Those  who  maintain  this  doctrine  are  perfectly  aware, 
of  course,  that  the  Predicate  is  sometimes  taken  universally 
in  Affirmative  Judgments,  as  when  we  predicate  either 
Definition  or  Property;  but  they  assert  that  this  results 
from  considering  the  Matter,  not  the  Form,  of  the  Judg- 
ment, and  therefore  is  not  entitled  to  notice  in  Pure  Logic. 
And  they  further  maintain,  that  the  Predicate  is  never 
quantified  particularly  in  a  Negative  Judgment.  Sir  W. 
Hamilton,  however,  as  we  shall  see,  has  denied  both  por- 
tions of  the  doctrine,  and,  by  substituting  for  it  his  own 
theory  of  "  the  thoroughgoing  quantification  of  the  Predi- 
cate," has  revolutionized  the  whole  science  of  Logic. 

In  respect  to  the  Relation  of  the  Predicate  to  the  Subject, 
Judgments  are  divided  into  simple  or  absolute,  and  con'- 
ditional.  In  the  former,  which  are  technically  called 
Categorical,  the  Predicate  is  conceived  as  a  Mark,  and  is 
therefore  absolutely  affirmed  or  denied  of  the  Subject, 
there  being  no  other  ground  or  reason  for  the  attribution 
or  denial  than  what  is  containe  I  in  the  Subject  itself.     All 


128  THE  DOCTRINE  OF  JUDGMENTS. 

Categorical  Judgments  are  included  under  these  two  for- 
mulas,  A  is  B,  A  is  not  B.  Conditional  Judgments  are 
those  in  which  the  Predicate  is  affirmed  or  denied  of  the 
Subject,  not  absolutely,  but  only  unde:  jome  condition 
or  prerequisite.  This  condition  may  be  conceived  as  pri- 
marily affecting  the  Subject,  or  the  Predicate,  or  both; 
and  hence  we  have  three  forms  of  Conditional  Judgments, 
distinguished  as  Hypothetical,  Disjunctive,  and  Dilemmatic 
or  Hypothetico-Disjunctive.  Thus,  in  respect  to  Relation, 
we  have  four  kinds  of  Judgments,  as  distinguished  in  the 
following  table. 

Categorical.  A  is  B,  or,  A  is  not  B. 

(  Hypothetical.  If  A  is  B,  A  is  C. 

C'mAY  alJ  ^%""diye-  A  is  either  B  or  C. 
'  \  Dilemmatic,  or 

(  Hypothetico-Disjunctive.  If  A  is  B,  then  C  is  either  D  or  E. 

In  a  Categorical  Judgment,  Man  is  mortal,  there  is 
evidently  no  ground  or  reason  for  the  attribution  but  an 
internal  one  ;  the  Mark  of  mortality  is  conceived  as  an 
essential  attribute  of  man  under  all  circumstances  or  con- 
ditions whatsoever.  But  in  each  of  the  other  forms,  the 
attribution  is  conditional.  In  the  Hypothetical  Judgment, 
Zf  death  is  a  transition  to  a  happier  life,  then  it  is  desirable, 
we  do  not  affirm  absolutely  that  death  is  desirable,  but 
affirm  it  only  under  a  condition  affecting  the  Subject, 
death.  In  a  Disjunctive,  as,  Every  deliberate  action  is  either 
good  or  evil,  the  condition  evidently  affects  the  Predicate, 
as  neither  of  its  two  forms  is  affirmed  absolutely,  but 
either  is  affirmed  only  on  condition  that  the  other  is  de- 
nied. The  Dilemmatic,  as  it  has  two  conditions,  the 
one  affecting  the  Subject  and  the  other  the  Predicate,  is 
obviously  a  combination  of  the  two  preceding  forms,  and 
is  therefore  properly  called  the  Hypothetico-Disjunctive. 
All  Hypothetical  Judgments  obviously  consist  of  two  parts, 
the  first  of  whici  is  called  the  Condition  or  Antecedent, 
and   the   secend,  the    Consequent;    and   the   assertion    or 


THEIR  QUANTITY,   QUALITY,   AND  RELATION.  129 

Judgment  is,  that  if  the  .Condition  exists,  the  Consequent 
follows. 

A  Conditional  Judgment,  though  seemingly  complex,  is 
really  simple,  and  expresses  only  a  single  act  of  Thought ; 
it  contains  but  one  assertion.  Thus,  in  the  Hypothetical 
just  cited,  we  do  not  assert  that  death  is  a  transition,  or 
that  death  is  desirable  ;  but  only,  if  it  is  a  transition,  then 
it  is  desirable.  Hence  the  affirmation  is  evidently  single, 
and  the  particles  if  and  then  form  the  Copula  of  this 
Judgment,  as  they  connect  its  two  parts  together.  In  a 
Disjunctive,  either  is  and  or  is  form  <ie  Copula,  which 
reduces  an  apparently  complex  Judgment  to  a  simp* 
Sometimes  where  and  there  take  the  place  of  if  and  then 
in  a  Conditional  Judgment ;  as,  where  fire  is,  there  is  heat ; 
where  light  is,  there  is  shadoiv. 

In  Hypothetical,  the  Consequence,  or  tie  which  binds 
together  the  Antecedent  and  the  Consequent,  may  be 
either  mediate  or  immediate.  It  is  Mediate,  only  when 
there  is  nothing  in  the  Terms  of  either  of  the  two  parts 
which  binds  them  together;  as  when  we  say, 

If  A  is  B,  C  is  D. 

If  the  air  is  still  and  cloudless,  the  dew  wiUfall. 
If  Grod  is  just,  sinners  will  be  punished. 

In  such  cases,  the  Consequence  may  be  valid,  but  it  is 
not  Immediate ;  for,  as  there  are  four  distinct  Terms,  the 
two  Parts  have  ho  common  Term,  and  are  therefore  con- 
nected only  by  some  unknown  cause,  or  by  what  is  in  the 
mind,  but  is  not  expressed.  The  unexpressed  medium, 
which  binds  the  two  Parts  together  in  the  last  case,  is  our 
knowledge  that  God  governs  the  world,  and  that  justice 
consists  in  rewarding  the  good  and  punishing  sinners;  there- 
fore, if  God  is  just,  sinners  will  be  punished. 

The  Consequence  is  Immediate,* when  there  are  only 
three  Terms  in  the  two  Parts,  so  that,  since  one  of  these 

6* 


130  THE  DOCTRINE  OF  JUDGMENTS. 

Terms  is  necessarily  repeated,  it  forms  an  immediate  con- 
nection of  the  Parts  with  each  other.  In  order  that 
there  may  be  this  repetition  of  one  of  the  Terms,  either 
the  two  Parts  must  have  the  same  Subject,  or  the  same 
Predicate,  or  the  Predicate  of  the  first  must  be  the 
Subject  of  the  second,  or  the  Subject  of  the  first  must 
be  the  Predicate  of  the  second.  In  other  words,  the 
Hypothetical  must  appear  under  one  of  the  four  following 
formulas. 

is  B,  A  is  C.  If  men  do  wrong,  they  deserve  pun- 
ishment. 

If  A  is  B,  C  is  B.  If  metals  are  fusible,  gold  is  fusible. 

If  A  is  B,  B  is  C.         If  patience  be  a  virtue,  virtue  may 

be  painful. 

If  A  is  B,  C  is  A.         If  happiness  is  mere  freedom  from 

pain,  insensibility  is  happiness. 

In  each  of  these  cases,  the  Consequence  is  Immediate, 
because  it  results  from  a  general  rule,  which  is  presupposed 
in  the  Proposition  that  is  before  us,  and  may  be  evolved 
from  it  without  any  further  appeal  to  experience.  Because 
44  all  C  is  A,"  we  can  immediately  infer  that,  "  if  A  is  B, 
C  is  B " ;  or  conversely,  because  the  latter  Proposition 
is  universally  true,  the  former  can  be  deduced  from  it  by 
necessary  implication.  If  the  earth  is  immovable,  and  is 
lighted  in  all  parts  by  the  sun,  the  sun  revolves  round  it ;  — 
tins  is  true  so  far  as  concerns  the  dependence  of  the  one 
Proposition  upon  the  other,  though  either  Proposition, 
taken  separately,  is  false.  Hence,  we  do  not  deny  a 
Hypothetical  Judgment  by  denying  either  or  both  of  its 
parts,  but  only  by  denying  the  Consequence  of  one  from 
the  other.  This  is  usually  done,  in  Latin,  by  placing  the 
negation  at  the  beginning. 

Non  si  miserum  fortuna  Sinonem 
Finxit,  Yanum  etiam  mendacemque  improba  finget 


THEIR  QUANTITY,   QUALITY,  AND  RELATION.  131 

In  English,  we  may  deny  a  Hypothetical  by  substituting 
although^  or  some  equivalent,  for  if  in  the  Reason,  and 
then  negativing  the  Consequent. 

If  you  eat  of  the  forbidden  fruit,  you  shall  die. 
Although  you  eat,  $r.,  yw  shall  not  die. 

Or  the  Proposition  may  bo  thus  denied. 

It  is  not  true  that  if  you  eat,  Src. 

Disjunctives  are  denied  in  the  same  manner. 

Conditional  Judgments  can  be  reduced  to  Categoricals, 
though,  for  logical  purposes,  it  is  more  convenient  to  retain 
them  in  the  Conditional  form.  The  Condition  is  equiva- 
lent to  a  limitation,  and  therefore  can  always  be  expressed 
by  a  limiting  adjective  (see  page  143).  In  the  formula, 
If  A  is  B,  then  A  is  C,  it  is  not  asserted  that  all  A  is  C, 
but  only  those  A  which  are  B.  Let  d  represent  such  A  ; 
then  the  equivalent  Categorical  formula  is,  dA  are  C 
To  take  a  concrete  instance :  —  If  the  iron  is  magnetic,  it 
las  the  attribute  of  polarity ;  this  is  equivalent  to  the 
Categorical  Judgment,  magnetic  iron  is  polar.  Conversely, 
if  any  Categorical  Judgment  has  its  Subject  limited  by  a 
qualifying  word,  the  limitation  can  be  resolved  into  a 
condition,  and  the  Judgment  thus  becomes  Conditional. 
Thus,  Virtuous  men  are  happy,  is  equivalent  to  If  men  are 
virtuous,  they  are  happy. 

Disjunctives  are  reduced  in  a  similar  manner  to  as  many 
Categoricals  as  there  are  disjunct  members  of  the  Predi- 
cate.    Thus,  — 

(  All  those  A  which  are  not  B  are  C, 
A  is  either  B  or  C  =  <  and 

(  All  those  A  which  are  not  C  are  B ; 

and  if  d  represents  the  former  and  /  the  latter,  we  have 
dA  are  C,  and  fA  are  B.  Even  then,  the  Thought  is  not 
complete  until  we  add,  dA  -f-  fA  =  all  A.  It  amounts 
to  the  same  thing  to  say,  that  a  Disjunctive  may  be  first 


132  THE  DOCTRINE  OF  JUDGMENTS. 

resolved  into  as  many  Hypotheticals  as  it  has  disjunct 
members;  and  each  of  these  may  then  be  reduced,  as 
before,  to  a  Categorical.  Thus,  If  A  is  not  B,  it  is  C ; 
and,  If  A  is  not  (7,  it  is  B.  Evidently,  then,  Disjunctives 
are  only  complex  Hypotheticals. 

3.     The  Hamiltonian  Doctrine  of  Judgments. 

According  to  the  Aristotelic  doctrine,  as  we  have  seen, 
in  all  Affirmative  Judgments,  the  Predicate  is  Particular, 
while  in  all  Negative  Judgments  it  is  Universal.  Thus 
we  have  but  four  fundamental  Judgments  or  Propositional 
Forms,  which  have  been  designated  by  the  four  vowels 
A,  E,  I,  and  O.  According  to  Sir  William  Hamilton's 
doctrine  of  "the  thorough-going  quantification  of  the 
Predicate,"  in  both  Affirmative  and  Negative  Judgments, 
the  Predicate  may  be  distributed  or  undistributed,  —  that 
is,  may  be  either  Universal  or  Particular.  This  doctrine 
gives  us  eight  Propositional  Forms,  which  are  thus  indi- 
cated :  —  A  signifies  that  the  Term  to  which  it  corresponds, 
whether  Subject  or  Predicate,  is  universal,  whilst  I  signifies 
that  it  is  particular;  /,*  standing  in  the  place  of  the 
Copula,  signifies  that  the  Judgment  is  affirmative,  whilst 
n  *  signifies  that  it  is  negative.  Thus  we  have  the  follow- 
ing table  of  Hamilton's  eight  fundamental  Judgments, 
those  of  them  which  are  recognized  under  the  Aristotelic 
doctrine  being  also  indicated,  as  before,  by  the  four  vowels. 

Affirmatives. 

Afa.    All  X  are  all  Y.       e.  g.  All  copperas  is  all  sulphate  of  iron.  (1.) 
(A.)  Afi.    All  X  are  some  Y.     "     All  whales  are  some  mammals.         (2.) 

Ifa.     Some  X  are  all  Y.     "     Some  men  are  all  logicians.  (3.) 

(I.)    Ifi.      Some  X  are  some  Y.  "     Some  quadrupeds  are  some  amphib- 
ious. (4.) 

*  These  two  letters  are  selected  because  they  are  the  two  first  consonants 
of  affirmo  and  nego. 


THE  HAMILTONIAN  ANALYSIS.  133 

Negatives. 

(B.)  Ana.    Not  any  X  is  any  Y.       e.  g.  Not  any  fish  is  any  warm- 
blooded. (5.) 
Ani.     Not  any  X  is  some  Y.        "     Not  any  Englishman  is  tome 

Briton  (Scotch).  (6.) 

(O.)  Ina.     Some  X  are  not  any  Y.     "     Some  Frenchmen  are  not  any 

Parisians.  (7.) 

Ini.       Some  X  are  not  some  Y.    "    Some  trees  (oaks)  are  not  some 

trees  (maples).  (8.) 

The  question  is,  whether  these  four  Forms,  viz.  Afa,  Ifa, 
Ani,  and  Ini,  which  have  been  added  to  the  list  by  Sir 
W.  Hamilton,  are  legitimate  and  natural  Forms  of  Thought, 
—  whether  we  do  not  have  frequent  occasion  to  think  them 
as  Judgments,  though  we  seldom  or  never  express  them  as 
Propositions.  It  is  admitted  that  the  predesignations  of 
quantity,  some,  all,  any,  here  italicized  as  belonging  to  the 
Predicate,  are  usually  elided  in  expression.  This  is  the  case 
even  with  the  old  Forms,  A,  E,  I,  and  O  ;  for  language 
aims  always  at  brevity,  and  therefore  usually  omits  all  that 
is  so  obvious  as  to  be  easily  understood,  since  its  expression 
would  only  cumber  and  lengthen  the  sentence  unnecessari- 
ly. Thus,  we  usually  say,  Men  are  animals  ;  but  nearly  all 
logicians  acknowledge  that  the  Thought,  of  which  this  is  an 
abbreviated  expression,  is,  All  men  are  some  animals.  But 
the  peculiar  function  of  Logic  is  to  analyze,  not  language, 
but  Thought ;  it  deals,  not  with  Propositions,  but  with  Judg 
ments.  Hence  its  necessary  postulate,  that  we  must  be 
allowed  to  express  logically  all  that  is  contained  in  what 
we  think.  The  question  is,  whether  we  are  not  often 
obliged  to  think  Judgments  under  the  Forms,  All  are  'all, 
Some  are  all,  Not  any  is  some,  and  Some  are  not  some. 

N:>w  the  evidence  in  favor  of  the  first  two  of  these 
Forms,  the  affirmatives  Afa  and  Ifa,  is  so  strong,  that  the 
only  wonder  is,  how  they  could  have  been  almost  univer- 
sally rejected  by  logicians  for  over  two  thousand  years, 
down  tc  the  time  of  Sir  W.  Hamilton.     In  the  first  place. 


134  THE  DOCTRINE  OF  JUDGMENTS. 

any  process  of  inductive  reasoning  can  be  properly  reduced 
to  logical  Form  only  in  this  manner :  — 

X,  Y,  Z,  &c.  are  B„ 

But  X,  Y,  Z,  &c.  are  (or  represent)  all  A. 

Therefore,  all  A  are  B. 

Here  the  second  premise  is  materially  false ;  but  with 
this  fault,  as  4ogicians,  we  have  nothing  to  do.  Logic  does 
not  guarantee  the  truth  of  the  premises,  but  only  the  validi- 
ty of  the  inference  from  the  premises  to  the  conclusion. 
And  that  this  inference  is  valid  in  the  preceding  formula 
may  be  seen  by  taking  an  instance  in  which  neither  of  the 
premises  is  faulty.  If  I  am  playing  chess,  and  my  king  is 
in  fatal  check,  I  must  reason  thus :  — 

I  can  neither  move  my  king,  nor  interpose  a  man,  nor 
capture  the  attacking  piece. 

But  these  three  are  all  the  modes  of  obviating  check. 

Then  I  am  checkmated. 

Here  the  Predicate  of  the  second  premise  is  quantified 
universally;  and  men  reason  in  this  manner  every  day, 
when  they  are  reduced  to  a  choice  among  a  few  only  possi- 
ble modes  of  action,  and  each  of  these  modes  is  fatal.  The 
following  example  shows  how  we  reason  inductively :  — 

Copper,  tin,  lead,  iron,  &c.  are  fusible. 

But  copper,  tin,  lead,  &c.  are  (or  represent)  all  metals. 

Then  all  metals  are  fusible. 

As  already  hinted,  every  adequate  Definition  —  that  is, 
every  one  in  which  the  Definiendum  and  the  Definition  are 
convertible  terms  —  has  its  Predicate  universally  quantified 
in  Thought.  To  take  the  instance  already  given,  All  cop- 
peras is  sulphate  of  iron,  or,  conversely,  All  sulphate  of  iron 
is  all  copperas.  So,  also,  every  exhaustive  Division  must 
be  thought  as  a  Judgment  with  a  universal  Predicate. 
Thus,  the  geometer,  having  demonstrated  a  certain  prop- 
osition successively  of  equilateral,  isosceles,  and  scalene 
triangles,  adds  in  Thought,  But  these  are  all  triangles; 
therefore,  the  theorem  holds  good  of  all  triangles. 


THE  HAMILTONIAN  ANALYSIS.  135 

*  In  fact,"  says  Hamilton,  "  ordinary  language  quantifies 
the  Predicate  so  often  as  this  determination  becomes  of  the 
smallest  import.  This  it  does  directly,  by  adding  all,  some, 
or  their  equivalent  predesignations,  to  the  Predicate ;  or  it 
accomplishes  the  same  end  indirectly,  in  an  exceptive  or 
limitative  form. 

ua)  Directly,  —  as,  Peter,  John,  James,  etc.  are  aU  the 
Apostles  ;  —  Mercury,  Venus,  etc.  are  all  the  planets. 

"  b)  But  this  is  more  frequently  accomplished  indirectly, 
by  the  equipollent  forms  of  Limitation  or  Inclusion,  and 
Exception.* 

"  For  example,  by  the  limitative  designations,  alone  or 
only,  we  say,  God  alone  is  good,  which  is  equivalent  to 
saying,  God  is  all  good,  that  is,  God  is  all  that  is  good; 
Virtue  is  the  only  nobility,  that  is,  Virtue  is  all  noble,  that 
is,  all  that  is  noble.  The  symbols  of  the  Catholic  and 
Protestant  divisions  of  Christianity  may  afford  us  a  logical 
illustration  of  the  point.  The  Catholics  say;  Faith,  Mope, 
and  Charity  alone  justify  ;  that  is,  the  three  heavenly  virtues 
together  are  all-justifying,  that  is,  all  that  justifies ;  omne 
justificans,  justum  faciens.  The  Protestants  say,  Faith 
alone  justifies  ;  that  is,  Faith,  which  they  hold  to  comprise 
the  other  two  virtues,  is  all-justifying,  that  is,  all  that 
justifies;  omne  justificans.  In  either  case,  if  we  translate 
the  watchwords  into  logical  simplicity,  the  predicate  ap- 
pears predesignated. 

"  Of  animals  man  alone  is  rational ;  that  is,  Man  is  all 
rational  animal.  What  is  rational  is  alone  or  only  risible  ; 
that  is,  All  rational  is  all  risible,  etc. 

"  I  now  pass  on  to  the  Exceptive  Form.  To  take  the 
motto  overhead,  —  ■  On  earth  there  is  nothing  great  but 
man.'     What  does  this  mean?     It  means,  Man  —  is  —  all 

*  The  English  Exclusive  particles  are,  one,  only,  alone,  exclusively,  pre- 
cisely, just,  sole,  solely,  nothing,  but,  &c.  These  particles  annexed' to  the  Sub- 
ject predesignate  the  Predicate  universally,  or  to  its  whole  extent 


136  THE  DOCTRINE   OF  JUDGMENTS. 

earthly  great.  {Homo  —  est  —  omne  magnum  terrestrt.) 
And  the  second  clause  — '  In  man  there  is  nothing  great 
but  mind'  —  in  like  manner  gives,  as  its  logical  equipollent, 
Mind — is —  all  humanly  great,  that  is,  all  that  is  great  in 
man.     (Mens  est  omne  magnum  humanum.y 

The  case  may  not  seem  so  clear  in  respect  to  the  two 
negative  Forms,  Ani  and  Ini,  in  which  the  Predicate  is 
Particular ;  for  the  expression  of  them  in  language  is  so 
awkward  and  unnatural  as  to  have  provoked  the  remark, 
that  they  seem  to  be  got  up  as  if  for  the  purpose  of  show- 
ing what  one  could  do.  It  would  certainly  be  accounted  a 
forced  and  uncouth  assertion,  to  say  that  not  any  iron  is 
some  metal,  —  i.  e.  is  not  lead ;  or  that  some  men  (English- 
men) are  not  some  men  (Frenchmen).  Dr.  Thomson  ad- 
mits that  they  are  conceivable,  but  denies  that  they  are 
actual,  cases  of  negative  predication.  He  argues  that 
"  such  a  Judgment  is  never  actually  made,  because  it  has 
the  semblance  only,  and  not  the  power,  of  a  denial.  True 
though  it  is,  it  does  not  prevent  our  making  another  Judg- 
ment of  the  affirmative  kind  from  the  same  Terms.'*  It 
would  be  more  correct  to  say  that  we  can  make  "  another 
Proposition,"  instead  of  "another  Judgment,"  from  the 
same  Terms  ;  for  the  "  some  metal "  in  the  Predicate  of  the 
negative  Judgment  is  not  thought  as  the  same  "some  metal" 
in  the  Predicate  of  the  affirmative.  The  two  assertions 
are  incompatible  in  Thought,  though  they  happen  to  be 
identical  in  expression.     Thus,  — 

Iron  is  not  some  metal,  —  i.  e.  is  not  lead. 

Iron  is  some  metal, — i.  e.  is  iron. 

Englishmen  are  not  some  men,  —  not  Frenchmen. 

Englishmen  are  some  men,  —  Englishmen. 

In  fact,  the  law  of  Division,  that  the  Dividing  Members 
must  exclude  each  other,  compels  us  to  think  some  are  noi 
some,  —  these  are  not  those,  —  these  are  different  from  those. 
As  already  shown,  negation  is  only  the  affirmation  of  dif- 


THE  HAMILTONIAN  ANALYSIS.  187 

ference  or  exclusion ;  '  A  is  not  B,'  is  equivalent  to  «  A  is 
not-B/  Now  we  never  have  occasion  to  affirm  difference 
or  exclusion  except  for  the  purpose  of  distinguishing  co- 
ordinate Species  from  each  other ;  for  if  the  two  classes  were 
not  recognized  as  belonging  to  the  same  Genus,  —  that  is, 
as  similar  in  some  respects,  —  it  would  not  be  necessary  to 
think  or  to  say  that  they  differ  in  certain  other  respects. 
We  never  say,  Fishes  are  not  stars,  since  the  two  things  are 
so  unlike  that  there  is  no  danger  of  confounding  them 
But  we  think  and  say,  Oaks  are  not  maples,  Spaniels  are 
not  terriers,  as  the  classes  are  here  thought  as  belonging  to 
the  same  proximate  Genera,  trees  and  dogs.  In  Thought, 
therefore,  these  two  Judgments  are  explicated  thus :  Some 
trees  are  not  some  trees;  Some  dogs  are  not  some  dogs. 

Even  the  Aristotelic  doctrine  admits  that  Unskilful  are 
some  physicians  is  a  legitimate  Judgment,  for  it  is  the  sim- 
ple converse  of  Some  physicians  are  unskilful.  But  it 
amounts  to  precisely  the  same  thing  whether  we  say,  Tin* 
skilful  are,  &c,  or  Not  (any)  skilful  are  some  physicians. 
Considered  as  Propositions,  one  of  these  may  be  con- 
demned as  faulty  in  expression ;  but  as  Judgments,  one 
cannot  be  admitted  and  the  other  rejected,  for  they  are  one 
and  the  same  Judgment. 

Again,  whenever  we  predicate  a  Genus  of  a  Species,  the 
Predicate  is  obviously  quantified  as  Particular ;  and  some, 
which  is  the  predesignation  of  particularity,  must  then  be 
thought  in  its  semi-definite  sense,  as  some,  excluding  all. 
In  this  sense,  we  cannot  think  that  some  are,  unless  we  also 
think  that  some  are  not.  Then,  every  such  Judgment 
carries  with  it  by  necessary  inference,  or  as  a  part  of  itself, 
another  Judgment,  negative  in  Form  and  with  a  Particular 
Predicate.  Thus  the  Judgment,  Men  are  some  animals 
(rational  bipeds),  is  incomplete  and  even  impossible  in 
Thought,  unless  we  also  think,  Men  are  not  some  (other)  ani- 
mals (brutes).    Either  of  these  two  assertions  thus  carrying 


138  THE  DOCTRINE   OF  JUDGMENTS. 

the  other  along  with  it  by  necessary  implication,  it  is  more 
natural  to  adopt  in  words  the  affirmative  form,  as  the  more 
frequent  and  familiar  one,  even  when  the  negative  meaning 
is  more  prominent  in  Thought.  As  Hamilton  remarks, 
"  men  naturally  preferred  to  attribute  positively  a  part  of 
one  notion  to  another,  than  to  deny  a  part." 

It  has  already  been  argued,  (page  110,)  that  although 
the  Predicate  in  any  Judgment  may  be  actually  thought 
only  connotatively,  or  as  a  Mark,  it  is  still  potentially  a 
Concept,  and  as  such,  it  denotes  a  class,  or  has  Extension. 
To  predicate,  therefore,  is  virtually  to  classify,  or  to  as- 
sign a  Subject  to  its  proper  place  in  a  class,  thereby  attrib- 
uting to  it  all  the  Marks  of  that  class.  Now  it  is  argued 
by  Mr.  Baynes,  with  great  force,  "  that  when  we  bring  an 
object  under  a  notion,  that  is,  when  we  predicate  of  it 
that  it  belongs  to  such  a  class,  we  must  know  that  it  occu- 
pies a  certain  place  in  that  class.  For  if  we  were  uncer- 
tain what  place  the  individual  object  occupied  in  the  class, 
or  whether  it  occupied  any  place  at  all,  we  should  not 
know  the  class,  and  could  not  therefore  bring  any  object 
under  it;  —  e.  g.  if  I  do  not  know  whether  rose  comes 
under  the  Concept  flower,  —  whether  it  is  equal  to  some 
part,  or  the  whole,  or  superior  to  it,  —  I  cannot,  of  course, 
predicate  flower  of  rose,  since  I  do  not  know  what  the 
Concept  means,  what  it  contains,  and  what  it  does  not. 
If,  therefore,  we  understand  the  object  at  all,  we  must  fix, 
in  Thought,  the  sphere  which  it  occupies  under  the  class  to 
which,  in  predication,  we  have  assigned  it.  In  other  words, 
if  we  comprehend  what  we  utter,  every  notion  holding  the 
place  of  predicate  in  a  proposition  must  have  a  determinate 
quantity  in  thought."  *  We  cannot,  for  instance,  predicate 
bird  successfully  of  pigeons,  of  winged  and  feathered  bipeds, 
and  of  animals,  unless  we  know  at  least  so  much  of  the 
characteristics  of  the  class  bird  as  to  be  able  to  think  that 

*  Baynes's  New  Analytic  of  Logical  Forms,  pp.  9,  10. 


THE  HAMILTONIAN  ANALYSIS.  139 

"  all  pigeons  are  some  birds,"  "  all  winged  and  feathered 
bipeds  are  all  birds,"  and  "some  animals  are  all  birds." 
In  like  manner,  we  cannot  exclude  a  Subject  from  a  given 
Concept  or  class,  —  as  when  we  say,  Whales  are  not  fish, 
unless  we  either  think  fish  as  cold-blooded,  vertebrated  ani- 
mals, living  in  the  water  and  breathing  by  gills,  in  which 
case  we  think  "  whales  are  not  any  fish  "  ;  or  accept  the 
vulgar  notion  of  fish  as  finned  animals  living  in  the  water, 
and  then  think  "  whales  are  not  some  fish,"  —  viz.  not  cold- 
blooded fish.  This  leads  us  to  remark,  that,  in  fact,  any  limi- 
tation of  the  predicated  class  by  a  limiting  adjective  is  equiv- 
alent to  quantifying  that  Predicate  particularly ;  —  e.  g. 
Pines  are  not  deciduous  trees  =  Pines  are  not  some  trees. 

These  reasons,  and  others  which  will  be  mentioned  when 
we  come  to  treat  of  Conversion,  seem  conclusive  in  favor 
of  Sir  W.  Hamilton's  doctrine,  that,  potentially  at  least, 
the  Predicate  is  always  quantified  either  universally  or  par- 
ticularly, both  in  affirmative  and  negative  Judgments. 

But  if  each  of  the  two  Terms  of  a  Judgment  has  its  own 
quantity  assigned  to  it  in  Thought,  then,  for  still  stronger 
reasons  than  those  which  have  already  (pp.  64,  110)  been 
assigned,  the  distinction  between  Subject  and  Predicate 
ceases  to  be  of  any  moment.  In  fact,  every  Judgment 
comes  from  an  act  of  comparing  two  quantified  Terms  with 
each  other ;  and  as  the  result  of  such  comparison,  we  have 
an  equation,  or  non-equation,  established  between  these 
Terms,  and  it  is  completely  indifferent  which  of  them  is 
placed  first.  Thus,  having  compared  two  Concepts,  A  and 
B,  I  find  either  that  they  agree,  or  do  hot  agree,  with  each 
other.  This  agreement  or  difference  may  be  expressed 
equally  well  in  either  of  the  following  formulas :  — 

A  is  B.  A  is  not  B. 

B  is  A.  B  is  not  A. 

A  and  B  are  equal.  A  and  B  are  not  equal. 

Convertible  or  equal  are  A  and  B.  Unconvertible  are  A  and  B. 


140  THE  DOCTRINE  OF  JUDGMENTS. 

In  these  last  two  formulas,  the  two  compared  notions  do 
not  stand  to  each  other  as  Subject  and  Predicate,  but  are, 
in  the  same  proposition,  either  both  Subjects  or  both  Predi 
cates. 

In  common  language,  if  the  two  Terms  are  both  quanti- 
fied universally  in  Thought,  it  is  admitted  to  be  of  no 
consequence  which  is  placed  first ;  usually,  that  which  is 
prior  or  pre-eminent  in  Thought  appears  as  the  Subject. 
Thus,  we  say  either,  Electricity  is  not  the  nervous  fluid,  or, 
The  nervous  fluid  is  not  electricity;  Common  salt  is  chloride 
of  sodium,  or,  Chloride  of  sodium  is  common  salt. 

But  if  the  two  Terms  differ  in  Quantity,  the  convenience 
of  language  requires,  in  most  cases  (not  in  all  *),  that  the 
one  which  has  the  wider  Extension  should  appear  as  the 
Predicate,  and  that  its  Quantity,  though  present  in  Thought, 
should  be  silently  passed  over  in  expression.  It  is  more  con- 
venient that  the  Term  which  has  the  less  Extension,  as  it  is 
more  definite  or  limited  in  meaning,  and  therefore  can  be 
more  easily  grasped  in  Thought,  should  be  placed  first ;  and 
then,  the  Quantity  of  the  Predicate,  as  it  is  known  to  be 
greater  than  that  of  the  Subject,  (and  it  matters  not  how 
much  greater  it  is,)  may  be  omitted  in  expression  for  the 
sake  of  brevity.  Metals  are  fusible  substances  is  a  shorter 
and  more  natural  expression  than  Some  fusible  substances 
are  metals,  though  the  two  propositions  convey  precisely 

*  Such  propositions  as  these,  for  instance,  are  common :  — 

It  is  disgraceful  to  be  a  slave  to  passion. 

Turpe  est  obsequi  libidini. 

Happy  is  he  who  is  able  to  know  the  causes  of  things. 

Felix  qui  potuit  rerum  cognoscere  causas. 

It  is  rain  which  has  fallen. 

It  is  foolish  to  listen  to  flatterers. 

If  the  Term  of  the  wider  Extension  must  be  the  Predicate,  we  should 
•ay,  —  To  be  a  slave  to  passion  is  disgraceful ;  He  who  can  discover  the  causes 
of  things  is  happy ;  That  which  has  fallen  is  rain ;  To  listen  to  flatterers  is 
folly. 


EXPLICATION   OF  PROPOSITIONS  INTO  JUDGMENTS.      141 

the  same  meaning.  Hence  the  old  logicians,  having  more 
regard  to  Language  than  to  Thought,  maintained  that  the 
former  order  was  the  only  legitimate  one ;  they  analyzed 
this  order  only,  and  based  upon  it  their  whole  system. 
"  Natural,  or  regular,  or  direct  predication  they  held  to  be 
that  in  which  the  genus  is  predicated  of  the  species,  the 
species  of  the  individual,  the  attribute  of  its  subject,  and, 
in  general,  the  extensive  whole  of  its  part ;  and  in  which, 
therefore,  the  Subject  notion  was  always  of  less  extent  than 
the  Predicate  notion.  Unnatural,  indirect,  or  irregular 
predication  was  the  reverse  of  this,  —  that,  to  wit,  in  which 
the  species  was  predicated  of  the  genus,  the  subject  of  its 
attribute,  and,  in  general,  the  extensive  part  of  its  whole."* 
But  when  it  is  acknowledged  that  Logic  has  to  do  pri- 
marily with  Thought,  and  only  secondarily  with  Lan- 
guage ;  that  each  of  the  two  Terms  has  its  own  Quantity 
assigned  to  it  in  Thought;  and  that  the  purport  of  the 
Judgment  is  merely  to  affirm  the  agreement  or  non-agree- 
ment of  these  two  quantified  Terms,  —  it  becomes  evi- 
dent that  every  proposition  is  logically  reduced  to  an 
equation,  or  non-equation,  of  two  Terms,  the  relative  posi- 
tion of  which  is  of  no  importance  whatever.  All  metals 
are  some  fusible  things,  and  Some  fusible  things  are  all  met- 
als, are  two  statements  of  precisely  the  same  import.  And 
in  like  manner  with  negatives;  —  Some  Frenchmen  are 
not  any  Parisians,  is  the  same  Judgment  as,  Not  any  Pa- 
risians are  some  Frenchmen, 

4.  The  Explication  of  Propositions  into  Judgments. 

Strictly  speaking,  as  we  have  seen,  Pure  Logic  deals 
only  with  Judgments,  and  refers  to  the  science  of  Lan- 
guage for  the  doctrine  of  Propositions,  or  the  proper  ex- 
pression of  Judgments  in  words.     But  the  claims  of  Logic 

*  Baynes's  Analytic,  p.  12. 


142  THE  DOCTRINE   OF  JUDGMENTS. 

to  be  regarded  as  a  universal  science,  and  its  doctrine  that 
all  Thought  can  be  reduced  to  distinct  Judgments,  so  that 
the  logical  theory  of  Judgments  is  applicable  to  every 
mental  product  into  which  Thought  enters,  cannot  be  de- 
fended, or  even  properly  understood,  until  it  is  clearly 
shown  how  all  Propositions,  even  the  most  complex  in 
character,  may  be  reduced  to  simple  Judgmenti.  We 
shall  therefore  consider  the  explication  of  Propositions 
here,  though  the  subject  properly  belongs  to  Applied 
Logic. 

Every  pure  Judgment  corresponds  to  one  of  these  two 
forms,  — A  is  B,  or  A  is  not  B ;  and  if  thus  expressed  in 
words,  it  is  called  a  Simple  Proposition.  In  this  case, 
neither  Subject  nor  Predicate  necessarily  consists  of  a 
single  word  ;  either  or  both  may  be  described  in  many 
words,  provided  that  the  union  of  these  words  expresses 
but  one  Judgment  or  a  single  act  of  Thought.  Thus,  Well 
organized  and  skilfully  administered  governments  are  produc- 
tive of  happiness  to  their  subjects,  is  a  Simple  Proposition,  as 
well  as  John  is  sick.  On  the  other  hand,  several  acts  of 
Thought  combined  in  one  statement  constitute  a  Compound 
Proposition,  the  plurality  of  which  may  reside  either  in  the 
Subject,  or  in  the  Predicate,  or  in  both.     Thus,  James  and 

William  are  young  and  healthy,  is  a  Compound  Proposition, 
which  may  be  resolved  into  these  four  Simple  ones:  — 
James  is  young;   James  is   healthy;    William  is  young ; 

William  is  healthy.  A  distinct  Judgment  is  evidently  ne- 
cessary for  each  of  these  affirmations,  whether  they  are 
expressed  separately,  or  united  into  one  Compound  Propo- 
sition. Such  a  Proposition  obviously  may  be  partly  true 
and  partly  false,  according  as  all,  or  only  some,  of  the  Predi- 
cates are  truly  affirmed  of  all,  or  only,  some,  of  the  Sub- 
jects. 

But  as  a  Simple  Proposition  contains  only  one  Subject 
and  one  Predicate,  it  would  seem  that  it  must  be  either 


EXPLICATION   OF  PROPOSITIONS  INTO  JUDGMENTS.       148 

wholly  true  or  wholly  false.  And  so  it  would  be,  but  thai 
Vhere  are  many  Propositions,  seemingly  Compound,  bu' 
really  Simple,  whose  Subject  or  Predicate  is  a  Complex 
term,  containing  by  implication  other  Judgments,  that  ma* 
be  called  incidental.  In  these,  the  incidental  Judgment 
may  be  false,  while  the  main  Proposition  may  be  true.  La 
those  which  are  properly  called  Complex  Propositions,  the 
incidental  or  implied  Judgment  may  appear,  either  as  a  part 
of  the  Subject  or  of  the  Predicate,  with  which  it  is  joined 
by  a  relative  pronoun,  whose  office  it  is  to  combine  several 
Propositions  into  one,  or  only  as  a  limiting  or  defining  ad- 
jective, or  participle,  or  adjective  clause.  Thus,  it  is  the 
same  thing  to  say,  God,  who  is  invisible,  created  the  world, 
which  is  visible;  or,  The  invisible  God  created  the  visiblt 
world.  It  is  justly  remarked  by  the  Port  Royal  Logi- 
cians, that  these  incidental  Judgments  are  to  be  regarded 
not  so  much  as  Propositions  which  we  now  make,  but  a? 
Judgments  formerly  made,  the  Predicate  of  which  is  now 
regarded  as  a  simple  Mark  or  attribute  of  one  of  the 
Terms  in  our  present  main  Proposition.  Hence  it  is  still 
true,  that  the  Complex  Proposition  is  Simple,  because  it 
expresses  but  one  Judgment  made  at  the  moment. 

The  incidental  Judgment  expressed  in  an  additional 
word  or  clause  may  be  either  explicative  or  limitative.  It  is 
Explicative,  when  it  is  of  the  nature  of  a  complete  or  partial 
definition,  and  therefore  belongs  to  the  Term  to  which  it  is 
annexed  in  the  whole  of  its  Extension.  Thus,  Man,  who 
is  born  of  woman,  is  of  few  days  and  full  of  trouble;  — 
here,  the  adjunct  clause,  born  of  woman,  is  to  be  understood 
as  a  definition  applicable  to  all  men.  But  in  such  a  Propo- 
sition as  this,  Men  who  are  avaricious  are  unhappy,  the 
relative  clause  restricts  or  limits  the  predication  of  unhap- 
piness  to  some  men,  —  to  those  only  who  are  avaricious. 
It  is  only  these  Complex  Limitative  Propositions  which  are 
equivalent  to  Hypotheticals :  —  thus,  All  iron  which  is  mag- 


144  THE  DOCTRINE  OF  JUDGMENTS. 

netic  is  polar,  has  the  same  meaning  as,  If  iron  is  mag- 
netic, it  is  polar.  It  depends  upon  the  Matter  of  the 
Thought,  and  can  usually  be  determined  by  the  context  or 
the  nature  of  the  subject,  whether  the  adjunct  word  or 
clause  is  to  be  considered  as  Explicative  .or  Limitative. 

With  regard  to  Explicatives,  it  should  be  observed,  that 
the  falsehood  of  the  incidental  does  not  affect  the  truth  of 
the  principal  Proposition.  Thus,  in  the  Proposition,  Har- 
modius  and  Aristogeiton  hilled  Hipparchus,  who  was  a 
tyrant,  or,  killed  the  tyrant  Hipparchus,  the  main  assertion 
would  still  be  true,  even  though  Hipparchus  was  not  a 
tyrant.  If,  however,  there  is  an  implied  Inference  or  ar- 
gument, that  the  principal  Proposition  is  true  because  the 
incidental  one  is  a  correct  definition,  then  the  falsity  of 
the  latter  becomes  a  reason  for  doubting,  not  for  denying, 
the  truth  of  the  former.  Thus,  the  Proposition,  Tlie  soul, 
which  is  an  extended  substance,  must  occupy  space,  becomes 
doubtful  when  the  incidental  affirmation,  that  it  is  extended, 
is  disproved;  but  it  may  still  be  true,  for  other  reasons, 
that  the  soul  must  have  some  position  in  space. 

In  respect  to  Limitatives,  no  question  can  arise  concern- 
ing the  truth  or  falsity  of  the  incidental  Proposition ;  for 
its  Predicate  is  not  affirmed  of  the  Subject  to  which  the 
relative  refers,  nor  is  the  existence  of  any  such  Subject 
affirmed.  If  I  say,  Judges  who  never  do  anything  by 
request  or  favor  are  worthy  of  praise,  the  only  assertion  is  a 
Hypothetical  one.  I  do  not  affirm,  that  Judges  never  do 
anything  by  request  or  favor,  or  that  there  are  any  such 
Judges ;  but  only,  that  if  there  are  any  such,  then  they  de- 
serve praise.  The  most  orthodox  believer  in  the  atoning 
virtue  of  the  death  of  Christ  may  still  admit,  that  a  man  who 
has  never  sinned,  and  is  not  sinful  by  nature,  stands  in  no 
need  of  art  atonement.  So  far,  indeed,  as  such  a  statement 
contains  any  implication  that  such  a  human  being  ever 
lived,  it  is  false ;  but  if  construed  strictly,  it  implies  noth- 
ing of  the  kind. 


EXPLICATION  OF  PROPOSITIONS  INTO  JUDGMENTS.       145 

Compound  Propositions  are  divided  into  those  which 
obviously  contain  a  plurality  of  Judgments,  and  therefore 
do  not  need  analysis  and  exposition;  and  those  in  which 
the  plurality  is  concealed,  so  that  it  is  apt  to  escape  notice. 
The  latter  are  called  Exponibles,  because  they  need  to  be 
analyzed  and  explained.  These  are  divided  into  Exclu- 
sives,  Exceptives,  and  Restrictives. 

Exclusive  Propositions  limit  the  Predicate  to  this  one 
Subject,  thereby  excluding  it  from  every  other  Subject. 
Hence,  every  Exclusive  contains  two  Propositions,  one  of 
which  affirms  the  Predicate  of  A,  and  the  other  denies  it 
of  all  not-A.     Thus, 

Only  A  is  B  =  j  ££*    fc  £ 

(  God  is  to  be  worshipped, 
God  alone  is  to  he  worshipped  =  <  JVo  other  being  is  to  be 

\      worshipped. 

Hamilton,  as  we  have  seen,  reduces  these  Compounds 
to  Simple  Propositions,  by  showing  that  the  Exclusive 
particle  annexed  to  the  Subject  quantifies  the  Predicate 
universally ;  thus :  — 

Only  A  is  B  =  A  is  all  B  ; 
whence  we  infer  immediately,  by  Infinitation,  that 
No  not-A  is  B. 

Sometimes  the  Exclusive  particles  only,  one,  sole,  &c, 
are  annexed  adjectively  to  the  Predicate,  and  then  have 
the  same  meaning  as  all.  Thus,  God  is  the  sole  object  to 
be  worshipped; — i.  e.  God  is  all  that  should  be  worshipped. 

Annexed  adverbially  to  the  Copula  and  Predicate  taken 
together,  the  Exclusive  particle  limits  the  Subject  to  tins 
one  Predicate,  thereby  excluding  it  from  every  other 
Predicate. 

Peter  only  plays  ;  i.  e.  he  plays,  and  he  does  nothing  else. 

James  is  only  a  lawyer ;  i.  e.  he  is  a  lawyer,  and  nothing 

else. 

7  * 


All  but  one  have  disappeared  = 


146  THE  DOCTRINE  OF  JUDGMENTS. 

But,  James  is  the  only  lawyer  =  he  is  all  the  lawyer  that 
vou  can  find. 

Exceptive  Propositions  state  the  Subject  universally,  yet 
with  a  specified  exception,  to  which  it  is  implied  that  the 
Predicate  is  not  attributed.  These  also  are  equivalent  to 
two  Judgments,  and  these  two,  as  in  the  case  of  Exclusives 
also,  differ  in  Quality. 

'  (Nearly)  all  have  disap- 
peared; 
but  one  has  not  disap- 
peared. 

In  respect  to  Quantity,  Exceptives  are  to  be  considered 
as  Universals.  For  although  a  part  is  excluded  from  the 
whole  of  the  Subject,  so  that  the  Predicate  is  referred 
only  to  the  remainder,  yet  this  remainder  constitutes  a 
whole  in  itself,  of  which  the  Predicate  is  affirmed  or 
denied. 

It  is  obvious  that  an  Exclusive  and  an  Exceptive  are 
only  two  modes  of  expressing  the  same  thing,  as  it  is  easy 
to  change  them  reciprocally  from  the  one  to  the  other ; 
but  the  direct  affirmation  in  one  becomes  the  implied 
assertion  in  the  other.  A  fool  thinks  that  no  method  ex- 
cept his  own  is  right;  in  other  words,  that  his  own  is  the 
only  right  method. 

Restrictive  Propositions  are  of  two  kinds,  both  of  which 
are  Limitative  in  meaning.  The  first  sort  restricts  the 
assertion  by  a  special  clause,  which  determines  more  nar- 
rowly the  signification  of  the  Subject  or  the  Predicate. 
Ethics,  considered  merely  as  a  doctrine  of  the  expedient,  is 
no  longer  a  science  of  morality :  —  this  is  equivalent  to 
the  two  Judgments,  Ethics  is  a  science  of  morality,  but 
a  mere  doctrine  of  expediency  is  not  such  a  science.  Here 
the  Subject  is  the  restricted  Term ;  but  in  the  following 
example,  it  is  the  Predicate.  A  good  magistrate  is  merci- 
ful to  offenders,  as  far  as  the  demands  of  justice  will  permit. 


EXPLICATION   OF  PROPOSITIONS  INTO  JUDGMENTS.      147 

The  second  sort  of  Restriction  is  called  Reduplicative,  as 
it  consists  in  a  repetition  of  the  restricted  Term.  A  judge, 
as  judge,  ought  never  to  receive  presents  ;  —  that  is,  he  may 
receive  them,  like  other  men,  on  ordinary  occasions,  but 
never  in  connection  with  the  performance  of  his  official 
duties.  Here,  also,  the  two  Judgments  into  wh'ch  the 
Proposition  is  explicated  differ  in  Quality. 


148  THE  DOCTRINE   OF  IMMEDIATE  INFERENCE. 


CHAPTER    VI. 

THE    DOCTRINE   OF  IMMEDIATE  INFERENCE.  ' 

1.   JEquipollence   or   Infinitation.  —  2.   Conversion.  —  3.  Opposition  and 
Integration. 

INFERENCE  or  Reasoning  is  that  act  of  Pure  Thought 
whereby  one  Judgment  is  derived  from  another,  or 
from  two  others.  The  Judgment  from  which  another  is 
deduced  is  called  the  Premise  ;  and  that  which  is  derived  ia 
called  the  Conclusion.  If  the  Conclusion  is  drawn  directly 
from  one  Premise  only,  without  the  aid  either  of  an 
Intuition  or  another  Judgment,  it  is  said  to  be  an  Immedi- 
ate Inference.  Thus,  from  the  Premise  that  No  quadruped 
is  rational,  I  know  at  once,  or  by  Immediate  Inference,  — 
that  is,  by  an  act  of  Pure  Thought,  —  that  Every  quadru- 
ped is  irrational,  and  that  No  rational  thing  is  a  quadruped. 
If  the  Conclusion  can  be  drawn  only  through  the  interven- 
tion of  a  third  Judgment,  —  in  other  words,  if  two  Prem- 
ises are  necessary,  —  the  result  is  a  Mediate  Inference, 
or  Syllogism. 

But  in  either  case,  the  act  of  Reasoning  or  Inference, 
whether  Mediate  or  Immediate,  is  simple,  being  one  indi- 
visible act  of  mind.  The  Premises  are  considered  as 
given,  and  their  truth  is  taken  for  granted ;  the  Inference 
is  the  act  of  deduction,  or  drawing  out  the  Conclusion  from 
the  Premises,  and  this  act  is  necessarily  simple.  If  it  is 
performed  in  accordance  with  the  Laws  of  Pure  Thought, 
it  is  apodeictic  or  absolutely  certain,  as  any  opposite  Con- 
clusion would  be  Contradictory  and  absurd.     In  respect  to 


THE  D03TRINE   OF  IMMEDIATE  INFERENCE.  149 

tneir  Matter,  both  the  Premises  and  the  Conclusion  may  be 
false  ;  and  yet  the  Form  of  Inference,  or  the  transition 
from  one  to  the  other,  may  be  intuitively  true.  Thus,  the 
Mediate  Inference, 

Everything  material  is  mortal; 

The  Soul  is  material; 

Therefore  the  Soul  is  mortal;  — 
is  false  in  each  of  its  three  Judgments.     Yet  its  Conclusion 
is  as  correctly  drawn,  and  the  Syllogism  is  therefore  just  as 
valid,  as  in  the  following  instance,  where  each. of  the  three 
Judgments  is  true. 

Everything  material  is  divisible  ; 

Gold  is  material ; 

Therefore  Gold  is  divisible. 
Hence,  the  material  truth  of  the  Conclusion  depends  upon 
the  material  truth  of  the  Premises ;  its  formal  validity  is 
the  correctness  of  the  process  whereby  it  was  deduced  from 
the  Premises.  Pure  Logic  has  to  do  only  with  the  latter. 
Every  correct  step  of  Reasoning,  considered  simply  as  such, 
or  in  reference  to  its  Form,  is  as  indisputable  as  one  of 
those  Primary  Axioms  of  Pure  Thought  on  which  it  is 
based,  or  of  which  it  is  an  application.  The  uncertainty  or 
disputable  character  of  much  of  what  is  improperly  called 
Reasoning  lies  altogether  in  the  Premises,  and  is  referable 
to  imperfect  observation,  to  an  improper  use  of  words  where 
language  has  become  a  substitute  for  Thought,  or  to  over- 
hasty  generalization.  But  the  mere  process  of  Reasoning, 
irrespective  of  the  data  about  which  we  reason,  is  the  same 
in  the  moral  and  physical,  as  in  the  purely  mathematical, 
sciences ;  it  is  equally  demonstrative  in  all,  for  it  is  condi- 
tioned by  the  absolute  laws  of  Pure  Thought.  The  long- 
est chain  of  argument  is  but  a  series  or  repetition  of  In- 
ferences, whether  Mediate  or  Immediate,  in  which  the 
formal  validity  of  each  step,  taken  by  itself,  is  intuitively 
p^r?eived. 


150  THE  DOCTRINE   OF  IMMEDIATE  INFERENCE. 

Logic,  as  Hamilton  remarks,  "  is  exclusively  conversant 
about  Thought  strictly  so  denominated ;  and  Thought 
proper,  we  have  seen,  is  the  cognition  of  one  object  of 
thought  by  another,  in  or  under  which  it  is  mentally  in- 
cluded ;  —  in  other  words,  Thought  is  the  knowledge  of 
a  thing  through  a  Concept  or  General  Notion,  or  of  one 
Notion  through  another.  In  Thought,  all  that  we  think 
about  is  considered  either  as  something  containing,  or  as 
something  contained ;  —  in  other  words,  every  process  of 
Thought  is  only  a  cognition  of  the  necessary  relations  of 
our  Concepts.  This  being  the  case,  it  need  not  move  our 
wonder  that  Logic,  within  its  proper  sphere,  is  of  such 
irrefragable  certainty,  that,  in  the  midst  of  all  the  revolu- 
tions of  philosophical  doctrines,  it  has  stood,  not  only 
anshattered,  but  unshaken.  In  this  respect,  Logic  and 
Mathematics  stand  alone  among  the  sciences,  and  their 
peculiar  certainty  flows  from  the  same  source.  Both  are 
conversant  about  the  relations  of  certain  a  'priori  forms  of 
intelligence;  —  Mathematics  about  the  necessary  forms  of 
Imagination ;  Logic  about  the  necessary  forms  of  Under- 
standing ;  —  Mathematics  about  the  relations  of  our  repre- 
sentations of  objects,  as  out  of  each  other  in  space  and  time ; 
Logic  about  the  relations  of  our  Concepts  of  objects,  as  in 
or  under  each  other,  that  is,  as  in  different  relations  respec- 
tively containing  and  contained.  Both  are  thus  demonstra- 
tive, or  absolutely  certain,  sciences,  only  as  each  develops 
what  is  given,  —  what  is  given  as  necessary,  in  the  mind 
itself.  The  laws  of  Logic  are  grounded  on  the  mere 
possibility  of  a  knowledge  through  the  Concepts  of  the 
Understanding,  and,  through  these,  we  know  only  by  com- 
prehending the  many  under  the  one.  Concerning  the 
nature  of  the  objects  delivered  by  the  Subsidiary  Faculties 
to  the  Elaborative,  Logic  pronounces  nothing,  but  restricts 
its  consideration  to  the  laws  according  to  which  their 
agreement  or  disagreement  is  affirmed." 


THE  DOCTRINE   OF  IMMEDIATE  INFERENCE.  151 

i4  It  is  of  itself  manifest  that  every  science  must  obey 
the  laws  of  Logic.  If  it  does  not,  such  pretended  science 
is  not  founded  on  reflection,  and  is  only  an  irrational 
absurdity.  All  Inference,  evolution,  concatenation,  is  con- 
ducted on  logical  principles,  —  principles  winch  are  ever 
valid,  ever  imperative,  ever  the  same.  But  an  extension  of 
any  science  through  Logic  is  absolutely  impossible ;  for  by 
conforming  to  logical  canons,  we  acquire  no  knowledge, 
receive  nothing  new,  but  are  only  enabled  to  render 
what  is  already  obtained  more  intelligible,  by  analysis  and 
arrangement.  Logic  is  only  the  negative  condition  of 
truth.  To  attempt  by  a  mere  logical  knowledge  to  amplify 
a  science,  is  an  absurdity  as  great  as  if  we  should  attempt, 
by  a  knowledge  of  the  grammatical  laws  of  a  language,  to 
discover  what  is  written  in  this  language,  without  a  perusal 
of  the  several  writings  themselves.  But  though  Logic 
cannot  extend,  cannot  amplify,  a  science  by  the  discovery 
of  new  facts,  it  is  not  to  be  supposed  that  it  does  not  con- 
tribute to  the  progress  of  science.  The  progress  of  the 
sciences  consists  not  merely  in  the  accumulation  of  new 
matter,  but  likewise  in  the  detection  of  the  relations  sub- 
sisting among  the  materials  accumulated ;  and  the  reflec- 
tive abstraction  by  which  this  is  effected  must  not  only 
follow  the  laws  of  Logic,  but  is  most  powerfully  cultivated 
by  the  habits  of  logical  study." 

Aristotle  has  defined  Inference  as  "a  thought  or  propo- 
sition in  which,  from  something  laid  down  and  admitted, 
something  distinct  from  what  we  have  laid  down  follows  of 
necessity."  But  this  definition,  though  it  describes  the 
Syllogism  accurately,  seems  at  first  to  be  inapplicable  to 
Immediate  Inference,  in  which,  as  there  is  only  one  premise, 
and  as  the  act  of  Pure  Thought  through  which  we  reason 
cannot  add  any  new  Matter  (that  is,  any  new  Intuition  or 
Concept),  it  would  appear  that  the  Conclusion  cannot  con- 
tain anything  distinct  from  what  has  already  been  laid  down. 


152  THE  DOCTRINE   OF  IMMEDIATE  INFERENCE. 

And  this  is  true  ;  it  cannot  contain  any  new  Matter,  but  n 
may  represent  this  Matter  under  a  new  Form,  so  that  the 
Conclusion  and  the  Premise  will  be  perfectly  distinct  Judg- 
ments. Thus,  in  the  instance  just  given,  "  quadruped " 
and  "  rational "  are  the  only  Terms  that  appear  in  either 
of  the  two  Conclusions,  "  irrational "  being  only  the  equiv- 
alent of  "  non-rational  "  ;  and  both  of  these  are  contained 
in  the  Premise.  And  yet  the  Inference  is  not  a  mere 
repetition,  but  the  Judgments  'which  it  involves  are  new 
and  distinct  from  what  was  previously  laid  down ;  for  one 
of  them  is  affirmative,  while  the  Premise  is  negative ;  and 
the  other  denies  a  certain  Mark  of  any  "  rational  thing," 
while  the  Premise  denies  a  certain  other  Mark  of  any 
"  quadruped."  If  it  be  argued  further,  that  such  Conclu- 
sions are  virtually  contained  in  the  Premise,  inasmuch  as 
they  become  evident  to  any  one  who  fully  apprehends  it, 
the  answer  is,  that  this  is  true  of  all  Reasoning,  even  of 
Syllogisms  and  Inductions.  That  a  certain  step  is  obvious 
and  easily  taken,  is  surely  no  proof  that  it  is  no  step  at  all, 
or  that  we  can  get  along  without  taking  it.  - 

1.    iEauiPOLLENCE  or  Infinitation. 

The  first  sort  of  Immediate  Inference  which  we  have  to 
consider  is  that  which  the  Greek  logicians  called  i<roSvvafit,a, 
and  the  Latins,  ^Equipollence ;  its  more  appropriate  name 
is  Infinitation.  It  has  already  been  said,  that  every  pair 
of  Concepts,  such  as  A  and  not-A,  of  which  one  is  merely 
the  Contradictory  or  the  privative  of  the  other,  divide  the 
universe  between  them.  According  to  the  axiom  of  Ex- 
cluded Middle,  either  A,  or  its  Infinitated  correlative,  not- 
A,  must  belong  to  everything,  and  must  include  everything ; 
and  according  to  the  axiom  of  Non-Contradiction,  the  pres- 
ence of  one  in  any  given  case  insures  the  exclusion  of  the 
other.      Hence  arise  a  number  of  Immediate  Inferences, 


^QUIPOLLENCE   OR  INFINITATION.  153 

soaie  of  which  are  of  frequent  occurrence  in  our  ordinary 
processes  of  thought.  As  already  remarked,  a  negative 
Judgment  can  always  be  changed  in  Form  to  an  affirma- 
tive, or  an  affirmative  to  a  negative,  simply  by  Infinitating 
one  of  its  Terms,  or  by  dropping  its  Infinitation ;  and  the 
result  is  a  new  Judgment,  the  truth  of  which  is  an  Imme- 
diate  Inference  from  the  truth  of  the  antecedent  Judgment 
whence  it  was  derived.  Here  the  Inference  is  only  an 
application  of  the  well-known  grammatical  rule,  that  two 
negatives  cancel  each  other,  and  thus  become  equivalent  to 
an  affirmative.  But  the  idiom  of  every  language  sanctions 
a  greater  or  smaller  number  of  exceptions  to  this  general 
rule,  none  of  which,  however,  are  admissible  in  Logic, 
where  every  negation  must  be  construed  rigorously. 

The  following  memoriter  lines,  which  I  copy  from  Bur- 
gersdyck,  enumerate  the  more  frequent  forms  of  asquipol- 
lence  and  of  the  idiomatic  force  of  negative  expressions ; 
but  of  course,  all  of  them  do  not  hold  good  in  this  meaning 
in  any  other  language  than  the  Latin. 

Non  omnis   =  quidam  non ;  omnis  non  quasi  nullus. 

Non  nullus  =  quidam  ;  sed  nullus  non  valet  omnis. 

Non  aliquis  =  nullus  ;  non  quidam  non  valet  omnis. 

Non  alter  s=  neuter ;  neuter  non  prcestat  uterque. 
In  all  cases  of  Immediate  Inference  by  Infinitation,  the 
dependence  of  the  Conclusion  upon  the  Premise  is  so  obvi- 
ous, and  so  directly  governed  by  the  Primary  Axioms  of 
Pure  Thought,  that  no  mistake  is  likely  to  arise,  except 
from  a  momentary  doubt  as  to  the  position  or  the  proper 
force  of  the  negative  particle.  The  two  following  rules 
comprehend  at  least  all  the  more  important  cases,  and 
they  hold  true,  I  believe,  without  exception,  for  the  four 
Propositional  Forms  which  are  recognized  in  the  Aris- 
totelic  system. 

Rule  I.     To  change  the  Infinitation  of  the  Predicate 

(either  by  Infinitating  if,  or  by  dropping  its  Infinita- 


154  THE  DOCTRINE   OF  IMMEDIATE  INFERENCE.     lj^ 

tion),  change  the    Quality  of  the  Judgment;  —  the 
Quantity  of  the  Judgment  then  remains  unaltered. 
Rule  II.     To  change  the  Infinitation  of  the  Subject, 
convert  the  Judgment  (i.  e.  make  the  Subject  and  the 
Predicate  change  places  with  each  other),  and  then 
either  change  the  Quality,  or  change  the  Infinitation 
of  the  (old)  Predicate  also; — here,  also,  the  Quantity 
of  the  Judgment  remains  unchanged. 
The  following  are  instances,  both  in  the  abstract  and  the 
•  terete,  of  the  application  of  these  two  Rules  to  all  four 
of  the  fundamental  Judgments,  A,  E,  I,  and  O,  and  also 
to  their  Infinitated  forms,  here  designated  as  A',  E',  I', 
and  O'.      Tins  enumeration  was  first   made    out  by  Mr. 
DeMonran.    It  will  be  seen  that  it  contains  no  instance  of 
mere  Conversion,  as  the  cases  under  that  head  will  be  after- 
wards separately  considered.     To  avoid  a  confusing  repeti- 
tion of  the  negative  particle  not,  words  compounded  with 
the  negative  prefixes  un  and  in  have  been  adopted  when- 
ever it  was  practicable.     For  the  same  reason,  right  is  used 
for  not-wrong ;  brutes  for  not-men;  pitiless  for  not-compas- 
sionate;  Ac.  ^  S 

Premises.  fc^*         Conclusions.  V-^ 

By  Rale  L  By  Rule  H. 

A.  Every  X  is  Y.        =  No  X  is  not-Y.  =  Every  not-Y  is  not-X. 

All  metals  are  ra>  ( =No  metal  is  infusi-  f  =  All   infusible   things    are 
sible.  (         ble.  (         unmetallic. 

O.  Some  X  are  not  Y.  =  Some  X  are  not-Y.    =  Some  not-Y  are  not  not-X 

Some  men  are  not  (  =  Some  men  are  piti-  <  =  Some  pitiless   beings  are 

compassionate.     \         less.*  (         not  mere  brutes  (not-men). 

E.  No  X  is  Y.  =  Every  X  is  not-Y.      =  Every  Y  is  not-X. 

No  avaricious  man  (  =  Every      avaricious  (  =  Every  happy  man  is  free 
is  happy.  \        man  is  unhappy.   {        from  avarice. 

*  Strictly  speaking,  or  according  to  the  rules  of  Logic,  "not-compassion- 
ate" has  the  same  meaning  as  "pitiless,"  for  it  is  the  contradictory  of 
"  compassionate."  But  in  common  parlance,  there  is  a  slight  difference  in 
the  meaning  of  the  two  words  ;  "  not-compassionate,"  like  most  other  epi- 
thets compounded  with  a  negative  particle,  means,  not  entire  privation  of  the 
quality,  but  only  the  existence  of  it  in  a  very  low  degree. 


£QUIPOI,LENCE   OR  INFINITATION.  155 

I.  Some  X  are  Y.        =  Some  X  are  not  not- Y.=  Some  Y  are  not  not-X. 
Some  wrong  acta  (  ==  Some   wrong   acts  <  =  Some  excusable  acts  are 
are  excusable.       \      are  not  inexcusable.  (        not  right  acts. 

A'.  Every  not-X  is  >       ,T        a  v  .    _.  ^         _  .    _ 

not-Y  C  =No  UDt"X  1S  Y*  =  Every  Y  is  X. 

Every  unjust   act  (=  No  unjust  act  is  ex- (=  Every   (truly)    expedient 
is  inexpedient.     (        pedient.  "|         act  is  just.* 

O'.  Some  not-X  are  >       0  .  v        ~  0         _,  .  _.. 

not  not-Y  ("  ==  ^ome  not_x  are  *  •    =  Some  Y  are  not  X. 

Some  invisible  things  (=  Some   invisible        (=  Some  tangible  things  are 
are  not  intangible.  (        things  are  tangible.  (         not  visible. 

B .  No  not-X  is  not  -Y.  =  Every  not-X  is  Y.      =  Every  not-Y  is  X. 


No  mortal  who-is-  ( =  Every  mortal  who- )       ,-,  .  ,      .    .,  . 

.     ,     .    .    •      )         .     J .     ,     _      .   (  =Every    mortal   who-is-in- 
not-a-brute  is  in-  -I         is-not-a-brute      is  > 

of  sin.      (        capable  of  sin.      ) 


not-a-orute  is  in-  •<         is-not-a-Drute      is  >  %,      -  .    .       ,  _ 

, ,      c  .  J  , ,      e    .         C         capable-of-sin  is  a  brute, 

capable  of  sin.      (        capable  of  sin.      )  * 


I'.  Some  not-X  are  )       Somenot.Xarenot  Y.=  Some  not-Y  are  not  X. 
not-Y.  \ 

Some  invertebrates  (  =Some  invertebrates  \  =Some    wingless    animals 
are  wingless.         \         are  not  winged.     \        are  not  vertebrates. 

The  Infinitation  of  the  four  additional  Judgments  first 
considered  by  Sir  W.  Hamilton  cannot  with  equal  facility- 
be  reduced  to  rule.  As  either  Afa  or  Afa'  is  a  perfect  ex- 
pression of  the  absolute  identity  of  what  the  two  Terms 
denote,  either  may  be  deduced  by  Infinitation  from  the 
other,  and,  by  the  same  means,  several  other  less  perfect 
expressions  of  the  same  identity  may  be  obtained.  But  of 
these  less  perfect  expressions  some  may  more  properly  be 
regarded  as  inferences  by  Subalter nation.     Thus,  — 

Afa.    AUX^areain       /  No  X  is  not-Y  )       (  Every  not-Y  is  not-X. 

*r,     An  ~.r        >  =  <  No  Y  is  not-X  S  =  ^AllXareY. 

alinnot  Y3"6  )       I  Ev<ay  not-Xis  n0t-Y  )       1  All  Y  are  X 
All  extended  are  all  divisible  =  All  unextended  are  all  indivisible. 

On  the  other  hand,  as  Ini  and  Ini'  are  indefinite  expres- 
sions of  the  partial  disagreement  of  the  two  Terms,  they 

*  Some  writers  upon  the  theory  of  morals,  who  have  strenuously  main- 
tained  that  "  no  unjust  act  is  expedient,"  have  yet  been  very  unwilling  to 
admit  that  "every  expedient  act  is  just."  Yet  the  latter  proposition  i*  a 
necessary  inference  from  the  former. 


156  THE  DOCTRINE   OF  IMMEDIATE  INFERENCE. 

yield  no  inferences  by  Infinitation  properly  so  called ; 
though,  if  some  be  taken  in  its  semi-definite  sense,  they 
yield  a  number  of  unimportant  inferences  by  what  Sir  W. 
Hamilton  calls  Integration. 

The  following  are  the  more  common  inferences  by  In* 
finitation  from  the  two  remaining  pairs  of  these  four  Judg- 
ments. In  these  it  will  be  observed  that  the  Quantity  of 
the  Conclusion  often  differs  from  that  of  the  Premise. 

Ifa.     Some  X  are  all  Y.       =  All  not-X  are  not-Y.     =  No  Y  is  not-X. 
Some  curviiinears are  (  —  All  rectilinears  are  (  =  No  circular  is  rec- 
all circulars.  (  notrcirculars.  \         tilinear. 

Aui.  No  X  is  some  Y.       j  =  ^^X  *"  not  i  =  Some Yare  not-X. 

No  tyrants  are  some  (=  Some  w.ho,  are  no*  }  -  Some    kings    are 
kings.  tyrannical  are  not  L        not_tyrann£al. 


Ifa'.    Some  not-X  are  all )        ,T    v  .        A  v  <  =  Some    not-X    are 

not-Y.  |  =  No  X  is  not-Y.         }  nQty> 

Some  unsentient  are  (  =  No  sentient  thing  is  (  =  Some     unsentient 
all  inorganic.  "[  inorganic.  {       are  not  organic. 

Ani'.  Not    any  not-X    is )        0         v  iV  e  *  «c       v 

J  .  v  y  =  Some  X  are  not  Y.      =  Some  not-Y  are  X. 

some  not-Y.  J 

Not  any  dishonest  is  (  =  Some  honest  are  not  C  =  Some     imprudent 
some  imprudent.     |  prudent.  (  are  honest. 

2.   Conversion. 

A  Judgment  is  said  to  be  converted  when  its  Subject 
awd  Predicate  have  been  made  to  change  places  with  each 
other.  Before  Conversion,  the  Judgment  is  called  the 
Convertend ;  after  Conversion,  it  is  the  Converse.  The 
logical  doctrine  of  Immediate  Inference  by  Conversion 
shows  us  when  and  why  the  truth  of  the  Converse  is  a 
necessary  consequence  of  the  truth  of  the  Convertend. 
In  other  words,  Logic  takes  notice  only  of  what  is  called 
illative  Conversion,  in  which  the  Convertend  and  the  Con- 
verse must  either  both  be  true,  or  both  be  false,  together. 
Thus,  the  Conversion  of  No  A  is  B,  into  No  B  is  JL,  is  illa- 
tive ;  we  can  say, 


CONVERSION.  157 

No  carnivorous  animal  is  ruminant ;     _ 

therefore,  No  ruminant  animal  is  carnivorous. 
But  the  Conversion  of  Some  A  are  not  B,  into  Some  B  are 
not  A,  is  not  illative  ;  because  we  can  say,  Some  men  are  not 
logicians,  it  does  not  follow  that  Some  logicians  are  not  men. 

In  Conversion  of  Judgments,  the  learner  must  remem- 
ber that  the  whole  Predicate  must  change  places  with  the 
whole  Subject;  —  that  is,  whatever  belongs  to  the  Predi- 
cate must  be  transferred  to  the  Subject's  place,  and  what- 
ever relates  to  the  Subject  to  the  Predicate's  place.  For 
example ;  —  Some  temple  is  in  the  city,  is  not  converted  into 
Some  city  is  in  the  temple,  but  into  Something  in  the  city  is 
a  temple.  Again,  —  the  Predicate  of  Every  old  man  has 
been  a  boy,  is  not  boy,  but  has  been  a  boy  ;  therefore,  it  is 
not  converted  into  Some  boy  has  been  an  old  man,  but  into 
Some  one  who  has  been  a  boy  is  an  old  man.  To  avoid  mis- 
takes of  thi^  sort,  every  proposition,  before  Conversion,  — 
or,  indeed,  before  it  is  subjected  to  any  logical  treatment 
whatever,  —  should  be  reduced  to  its  simplest  logical  form, 
—  that  is,  to  the  formula  A  is  B,  or  A  is  not  B.  Then  no 
error  can  arise,  if  we  remember  that  all  which  precedes  the 
Copula,  is  or  is  not,  is  the  Subject,  and  that  all  which  fol- 
lows the  Copula  is  Predicate. 

In  treating  of  Conversion,  as  well  as  in  other  portions  of 
the  subject,  we  first  consider  exclusively  the  doctrine  of  the 
Aristotelic  system,  which  admits  only  of  four  fundamental 
Judgments,  and  reserve  for  subsequent  treatment  the 
Hamiltonian  theory  of  eight  Judgments. 

There  are  three  sorts  of  Conversion.  The  first  is  appli- 
cable to  E  and  I,  Universal  Negatives  and  Particular 
Affirmatives,  and  is  called  Simple  Conversion,  because  both 
the  Quantity  and  the  Quality  of  the  Judgment  remain  un- 
changed ;  that  is,  E  is  converted  into  E,  and  I  into  I.  If 
it  is  true  that  No  man  is  immortal,  it  follows  by  Immediate 
Inference  that  No  immortal  is  man  ;  for  if  any  one  immor- 


158  THE  DOCTRINE   OF  IMMEDIATE  INFERENCE. 

tal  were  a  man,  it  would  not  be  true  that  No  man  is  im- 
mortal. Likewise,  if  Some  men  are  just,  it  follows  imme- 
diately that  Some  just  beings  are  men  ;  because  the  assertion 
that  No  just  being  is  a  man,  would  contradict  the  Con- 
vertend.  By  Simple-  Conversion,  then,  a  Universal  Nega- 
tive passes  over  into  a  Universal  Negative,  and  a  Particular 
Affirmative  into  a  Particular  Affirmative. 

The  second  sort  is  Conversion  per  accidens,  in  which  the 
Quantity  is  changed  from  Universal  to  Particular,  but  the 
Quality  remains  unaltered.  This  is  applicable  to  A,  and 
also  may  be  applied  to  E,  though  the  latter,  as  we  have 
just  seen,  may  also  be  converted  simply.  But  A  cannot 
be  converted  simply ;  because,  though  all  men  are  animals, 
it  does  not  follow  that  all  animals  are  men.  The  Judgment 
in  the  Convertend  is,  that  men  are  included  under  the  class 
of  animals,  not  that  they  constitute  all  animals  ;  they  are 
only  some  animals.  Hence  the  Converse  is,  Some  animals 
are  men.  We  have  already  seen  that  E  is  converted  sim- 
ply into  E ;  but  O  also  is  obtained  by  Immediate  Inference 
from  E;  for,  if  None  are,  it  follows  that  Some  are  not. 
Hence,  the  Convertend,  No  man  is  immortal,  yields  as  its 
Converse,  not  only  E,  No  immortal  is  man,  but  O,  Some 
immortals  are  not  men.  Conversion  per  accidens,  then, 
changes  A  into  I,  and  E  into  O,  the  Quantity  in  both 
cases  being  diminished,  but  the  Quality  remaining  un- 
changed. 

The  Judgment  O  remains,  and  this  cannot  be  converted 
either  simply  or  per  accidens.  From  the  Convertend, 
Some  men  are  not  learned,  we  cannot  infer  that  Some 
learned  beings  are  not  men.  Indeed,  properly  speaking, 
O  cannot  be  converted  at  all  on  the  Aristotelic  system ; 
but  by  an  artifice  which  is  called  Contraposition,  the  third 
sort  of  Conversion,  another  Judgment  can  be  inferred 
from  it,  which  is  called  its  Converse,  though  it  is  prop- 
erly the  Converse  of  its  ^Equipollent  or  Jnfinitated  equiv- 


CONVERSION.  159 

alent.  In  order  to  convert  by  Contraposition,  then,  first 
infill  itate  the  Convertend  by  Rule  First,  and  then  convert 
simply.     Thus,  — 

Convertend.  Some  A  are  not  B.       Some  men  are  not  learned. 

Infinitated  equivalent.     Some  A  are  not-B.       Some  men  are  unlearned. 
Converse  of  this.  Some  not-B  are  A.       Some  unlearned  persons  are  men. 

Hence  I  is  the  Converse  by  Contraposition  of  O ;  and 
in  like  manner,  A  by  Contraposition  yields  E,  the  effect 
of  this  sort  of  Conversion  being  to  change  the  Quality  of 
the  Convertend,  while  its  Quantity  remains  unaltered.  A 
is  thus  contraponed :  — 

Convertend.  All  A  is  B.  All  men  are  rational. 

Infinitated  equivalent.    No  A  is  not-B.  No  man  is  irrational. 

Converse  of  this.  No  not-B  is  A.  No  irrational  being  is  a  man. 

No  inference  can  be  obtained  from  I  by  Contraposition ; 
for  if  infinitated,  I  becomes  O,  which  cannot  be  converted 
except  by  infinitating  it  back  again.  Logicians  seem  to 
have  overlooked  the  fact  that  E  can  be  contraponed  into 
I,  though  the  inferred  Judgment  in  this  case,  because  its 
Quantity  is  diminished,  is  weak  and  comparatively  worth- 
less.    Thus,  — 

No  A  is  B.  No  fish  is  warm-blooded. 

Every  A  is  not-B.  Every  fish  is  cold-blooded. 

Some  not-B  are  A.  Some  cold-blooded  animals  are  fishes. 

The  results  of  the  three  sorts  of  Conversion  have  been 
summed  up  in  this  (nonsense)  mnemonic  line,  in  which 
each  dissyllable  contains  the  vowel-symbol  first  of  the  Con- 
vertend and  then  of  its  Converse ;  and  each  pair  of  these 
dissyllables  is  followed  by  the  (italicized)  abbreviation  of 
the  kind  of  Conversion  by  which  the  two  preceding  infer- 
ences have  been  obtained ;  simp.  =  Simple  ;  Ace.  =  per 
accidens;  and   Cont.  =  Contraposition. 

Ecce  tibi,  simp. ;  armi-geros,  ace. ;  ante  boni,  Cont. 

The  same  thing  is  more  briefly  indicated  in  these  two 
Latin  words,  Hoc  capessit,  in  which  oc-ca  signifies  that  O 
and  A  are  converted  by  Contraposition ;  ape,  A  and  E  ^?er 
accidens ;  essi,  E  and  I  simply. 


160  THE  DOCTRINE   OF  IMMEDIATE  INFERENCE. 

The  most  striking  merit  of  Sir  W.  Hamilton's  system  of 
the  thorough-going  quantification  of  the  Predicate  is,  that 
it  abolishes  at  once  this  whole  cumbrous  system  of  Con- 
version in  three  kinds,  with  its  attendant  rules,  and  sub- 
stitutes for  it  the  universal  and  self-evident  process  of  Sim- 
ple Conversion.  As  it  has  already  been  demonstrated,  that 
each  Term  of  every  Judgment  has  its  own  Quantity  in 
Thought,  and  consequently,  that  the  distinction  of  Subject 
and  Predicate  may  be,  for  most  logical  purposes,  left  en- 
tirely out  of  view,  every  Judgment  being  reduced  to  an 
equation,  in  which,  of  course,  it  makes  no  difference  which 
of  the  equated  quantities  is  placed  first,  Conversion  be- 
comes at  once  a  simple,  uniform,  and  self-evident  process 
As  an  old  logician  (Du  Hamel,  as  quoted  by  Mr.  Baynes), 
remarks,  "  omnes  conversionum  leges  pendent  a  cohsesione, 
vel  potius  ab  identitate,  subjecti  et  attributi ;  quod  si  enim 
subjectum  conjungitur  et  identificatur,  ut  aiunt,  cum  attri- 
bute, necesse  est  pariter  attributum  uniri  et  identificari 
cum  subjecto."  Though  it  is  hardly  necessary  even  for 
the  youngest  learner,  I  give  examples  of  the  Hamiltonian 
mode  of  converting  each  of  the  eight  Judgments. 

Converted.  Converse. 

Afa.           All  rational  are  all  moral  (  =  Afa.  All  moral  are  all  rational 

beings                             (  beings. 

Afi  (A).     All  lilies  are  (some)  fra-  (  =  Ifa.  Some  fragrant  things  are  all 

grant                             (  lilies. 

Ifa.             Some  plants  are  all  trees    =  Afi.  All  trees  are  (some)  plants. 

Ifi  (1).        Some  vicious  men  are  rich  =  Ifi.  Some  rich  men  are  vicious. 

a       /-en    xr    ~  *.<. —  u~i/  (  =  Ana.    Nothing  that  can  move  itself 

Ana  (E).  No  matter  can  move  itseir  1 

v     '  (is  matter. 

Ani.           Not  (any)  indistinct  are  (  =  Ina.  Some  sounds  are  not  indis- 

some  sounds                  (  tinct. 

Ina  (O).    Some  virtuous  men  are  (  ==  Ani.  Not  (any)  happy  are  some 

not  happy                      \  virtuous  men. 

Ini.             Some  singers  are  not  some  (  =  Ini.  Some    musicians    are    not 

(good)  musicians          |  some  singers. 

Conversion  per  accidens,  says  Mr.  Mansel,  is  so  called 


CONVERSION.  161 

because  it  is  not  a  Conversion  of  the  Universal  per  se,  but 
only  of  the  Particular  which  happens  to  be  included  in  the 
Universal.  "  Some  B  is  A,"  is  primarily  the  Converse  of 
"  Some  A  is  B,"  and  only  secondarily  of  "  All  A  is  B,"  or 
because  "  All  A  "  includes  "  Some  A."  Properly  speak- 
ing, then,  it  is  no  Conversion  at  all,  but  only  an  Immediate 
Inference  by  Subalternation  from  the  proper  Converse. 
This  is  clearly  seen  in  the  case  of  the  Universal  Negative, 
E ;  No  A  is  B^  is  first  converted  into  E,  No  B  is  A,  whence 
we  obtain  by  Subalternation  O,  Some  B  are  not  A. 

Moreover,  it  is  evident  that,  by  reconverting  the  Con- 
verse, we  ought  to  regain  the  Convertend.  But  this  can- 
not be  done  after  converting  per  accidens  ;  we  first  convert 
A  into  I,  and  then  reconvert  I,  not  into  A,  but  into  I. 
For  example ;  —  All  men  are  mortal,  yields«by  accidental 
Conversion,  Some  mortals  are  men  ;  and  this  is  reconverted 
simply  into  Some  men  are  mortals. 

It  is  further  argued  by  Hamilton,  that  the  Aristotelic 
doctrine  applies  Conversion  to  the  naked  Terms  only, — 
to  the  Subject  and  Predicate  of  the  Convertend  without 
regard  to  the  Quantity  of  either ;  it  thus  changes  all  to 
some,  and,  as  we  have  just  seen,  it  makes  the  total  Quan- 
tity of  the  Converse  inferior  to  that  of  the  Convertend. 
But  this  is  evidently  wrong ;  for  the  quantified  Terms  are 
the  Concepts  which  were  compared  in  Thought  in  the 
Convertend,  and  these  only  ought  to  appear  after  Conver- 
sion, and  appear  unchanged.  Contraposition,  as  we  have 
already  shown,  is  a  mediate  process,  the  Conversion  being 
possible  only  through  a  previous  Infinitation ;  for  the  origi- 
nal Judgment,  on  the  Aristotelic  doctrine,  is  not  convert- 
ible at  all.  But  as  every  Judgment  is  certainly  the  result 
of  a  comparison,  to  assert  that  it  is  inconvertible,  is  to 
maintain  that  A  can  be  compared  with  B,  while,  at  the 
same  moment,  B  is  not  compared  with  A;  —  which  is 
absurd.     Comparison  is  necessarily  bilateral. 


162  THE   DOCTRINE   OF   IMMEDIATE   INFERENCE. 

3.    Opposition  and  Integration. 

Opposition  is  said  to  exist  between  Judgments  which 
have  the  same  Matter  (i.  e.  the  same  naked  or  unquali- 
fied Subject  and  Predicate),  but  differ  in  Quantity,  or  in 
Quality,  or  in  both.  The  logical  doctrine  of  Opposition 
shows  us  what  can  be  immediately  inferred  as  to  the  truth 
or  falsity  of  one  Judgment,  from  positing  or  sublating 
(i.  e.  affirming  or  denying)  one  of  its  Opposites.  Thus, 
from  positing  E,  No  A  is  B,  I  can  immediately  infer  the 
truth  of  its  Subaltern  Opposite,  O,  Some  A  are  not  B,  and 
the  falsity  of  its  Contradictory  Opposite,  I,  Some  A  are  B ; 
but  I  cannot  infer,  from  sublating  E,  the  truth  of  its  Con- 
trary Opposite,  A,  All  A  are  B. 

But  here  the  word  Opposition  must  be  taken  in  a  tech- 
nical and  qualified  sense.  It  was  first  applied  only  to  the 
relations  between  two  Contraries,  or  two  Contradictories ; 
and  this  is  its  proper  or  strict  meaning,  as  any  two  such 
Judgments  are  opposed  to  each  other,  the  one  negativing 
the  other,  and  it  is  impossible  that  the  two  should  be  true 
together.  But  as  it  was  convenient  for  Logicians  to  con- 
sider the  relations  of  Subalternation  and  Sub-Contrariety 
under  the  same  head  with  the  two  former,  the  meaning  of 
the  word  was  extended  so  as  to  cover  all  the  relations 
existing  between  two  Judgments  of  the  same  Matter,  but 
of  different  Form,  although  some  of  these  are  relations  not 
of  opposition,  but  of  congruity. 

There  are  four  sorts  of  Opposition.  The  first  and  most 
perfect  of  these  is  that  of  Contradiction^  which  exists  be- 
tween two  Judgments  which  differ  from  each  other  both  in 
Quantity  and  Quality ;  that  is,  between  A  and  O,  and  be- 
tween E  and  I.  This  sort  of  Opposition  is  governed  by 
the  Axiom  of  Excluded  Middle,  which  declares  that  of 
two  Contradictories,  —  that  is,  of  two  Judgments  between 
which  there  is  no  "  Middle,"  no  intermediate  Judgment,  — 


OPPOSITION  AND  INTEGRATION.  163 

one  must  be  true ;  and  then  the  Axiom  of  Non-Contra- 
diction adds,  that  the  other  must  be  false.     Now,  A  and 

0  are  two  such  Judgments,  and  likewise  E  and  I ;  so  also 
the  two  Singular  Judgments,  Socrates  is  wise,  and  Socrates 
is  not  wise.  Between  either  of  these  pairs,  no  4<  third  "  or 
intermediate  Judgment  is  conceivable.  Hence  the  univer- 
sal rule  for  this  sort  of  Opposition,  that  Contradictories  can- 
not both  be  true,  and  cannot  both  be  false.  Therefore,  as 
both  cannot  be  true,  if  I  posit  (affirm)  one,  I  immediately 
infer  that  the  other  is  sublated  (denied)  ;  and  as  both  can- 
not be  false,  if  I  sublate  one,  the  other  is  posited.  For 
example ;  —  if  E  is  not  true,  that  No  quadruped  is  rational, 

1  must  be  tru^,  that  Some  quadrupeds  are  rational. 

Observe  that  two  Judgments  properly  contradict  each 
other  only  when  that  which  is  affirmed  by  the  one  is  de- 
nied by  the  other,  —  1.  in  tlie  same  manner  ;  2.  in  the  same 
respect;  3.  in  the  same  degree;  and  4.  at  the  same  time. 
Thus,  to  borrow  some  examples  from  Aldrich,  —  1.  A  dead 
body  is,  and  is  not,  a  man ;  that  is,  it  is  a  dead  man,  but 
not  a  living  one.  2.  Zoilus  is,  and  is  not,  black ;  that  is, 
black-haired,  but  red-faced.  3.  Socrates  is,  and  is  not, 
long-haired  ;  that  is,  he  is  so,  if  you  compare  him  with 
Scipio,  but  is  not  so,  if  you  compare  him  with  Xenophon. 
4.  Nestor  is,  and  is  not,  an  old  man,  according  as  you 
speak  of  him  when  in  childhood,  or  when  he  was  at  the 
siege  of  Troy. 

The  second  sort  of  Opposition  is  that  of  Contrariety, 
which  exists  between  two  Universal  Judgments,  that  differ 
in  Quality,  but  are  alike  in  Quantity  ;  that  is,  between  A 
and  E.  Here  the  Axiom  of  Excluded  Middle  does  not 
apply ;  for  between  A  and  E,  there  is  a  "  Middle "  or 
intermediate  Judgment,  namely,  I.  Though  it  is  not  true, 
either  that  all  men  are  wise,  or  that  no  man  is  wise,  it  is 
true  that  some  men  are  wise.  Hence  both  Contraries  may 
be  false,  so  that  I  cannot  infer  the  truth  of  one  from  the 


164  THE   DOCTRINE   OF   IMMEDIATE   INFERENCE. 

falsity  of  the  other.  On  the  other  hand,  as  one  of  these 
Contraries  affirms  what  the  other  denies,  the  Axiom  of 
Non-Contradiction  applies ;  both  Contraries  cannot  be  true  ; 
and,  therefore,  from  the  truth  of  one  I  can  immediately 
infer  the  falsity  of  the  other.  Accordingly,  the  rule  is, 
Contraries  may  be  false  together,  but  both  cannot  be  true. 
Therefore,  from  positing  either  A  or  E,  I  can  immediately 
infer  that  the  other  is  sublated ;  but  from  sublating  either, 
I  cannot  infer  that  the  other  is  posited. 

The  third  sort  of  Opposition  is  that  of  Sub- Contrariety, 
which  exists  between  two  Particular  Judgments,  that  differ 
in  Quality,  but  are  alike  in  Quantity ;  that  is,  between  I 
and  O.  To  these,  the  Axiom  of  Excluded  Middle  is 
applicable  ;  for  there  is  no  third,  or  intermediate,  Judgment 
conceivable  between  Some  are,  and  Some  are  not.  Accord- 
ingly, both  cannot  be  false,  but  one  must  be  true.  On  the 
other  hand,  if  I  and  O  are  considered  as  Propositions,  that 
is,  if  the  Judgments  are  expressed  in  words,  the  Axiom  of 
Non-Contradiction  does  not  apply  to  them ;  for  both  may 
be  true.  Though  some  men  are  learned,  it  is  also  true  that 
some  men  are  not  learned.  But  observe,  that  the  "  some 
men  "  in  the  latter  case  are  not  the  same  "  some  men  "  as 
in  the  former ;  though  expressed  by  the  same  words,  they 
are  thought  as  different.  To  make  the  former  Proposition 
true,  "  some  men  "  may  be  thought  to  be  "  graduates  of 
Oxford  "  ;  to  make  the  latter  true,  "  some  men "  may 
mean  "  American  Indians."  As  Propositions,  then,  and 
possibly  as  Judgments,  the  two  assertions  do  not  contradict 
each  other,  but  may  both  be  true.  Hence  the  rule,  that 
Sub- Contraries  may  be  true  together,  but  cannot  both  be  false. 
Therefore,  by  sublating  either  I  or  O,  we  immediately  infer 
that  the  other  is  posited ;  but  by  positing  either,  we  can- 
not infer  that  the  other  is  sublated.  Of  course,  Sub- 
Contraries  can  be  called  "  opposites "  only  in  a  qualified 
and  technical   sense ;   they  are  actually  congruent,  or,  to 


OPPOSITION  AND  INTEGRATION.  165 

adopt  one  of  Hamilton's  newly-coined  words,  they  are 
"  compossible." 

The  fourth  sort  of  Opposition  is  that  of  Subalternation, 
which  exists  between  Judgments  alike  in  Quality,  but  dif- 
ferent in  Quantity ;  that  is,  between  A  and  I,  and  between 
E  and  O.  Here,  again,  it  is  evident  that  the  "  Opposi- 
tion "  is  merely  technical,  the  two  Judgments  being  not 
merely  consistent,  but  so  nearly  allied  that  the  Particular 
can  be  inferred  from  its  Universal  by  the  Axiom  of  Iden- 
tity. Since  all  includes  some,  if  we  affirm  A,  All  A  are  B, 
we  thereby  also  affirm  I,  Some  A  are  B  ;  and  in  like  man- 
ner, to  posit  E  is  also  to  posit  O.  The  same  Axiom  com- 
pels us  to  think,  that  sublating  I  sublates  A  also,  and 
sublating  O  sublates  E  also.  In  this  sort  of  inference,  the 
Universal  may  be  called  the  Subalternans,  and  the  Particu- 
lar, the  Subalternate.  Hence  we  have  this  rule  for  infer- 
ence by  Subalternation,  that  if  the  Subalternans  is  true,  the 
Subalternate  is  true  also ;  and  if  the  Subalternate  is  false, 
the  Subalternans  is  false  also. 

Summing  up,  we  have  the  following  list  of  Immediate 
Inferences  by  Opposition. 

!If  A  is  true,  O  is  false,  E  false,  and  I  true. 
If  E  is  true,  I  is  false,  A  false,"  and  O  true. 
(  If  I  is  false,  E  is  true,  O  true,  and  A  false, 
f  If  O  is  false,  A  is  true,  I  true,  and  E  false. 
If  A  is  false,  O  is  true,  )  ^  otherg  unknown. 
If  E  is  false,  I  is  true,    ) 
If  I  is  true,  E  is  false,    J  fte  otherg  unknown. 
If  O  is  true,  A  is  false,  ) 
Hence  it  appears,  that  from  the  truth  of  a  Universal  or 
the  falsehood  of  a  Particular,  we  may  infer  the  character  of 
all  the  opposed  Judgments ;  but  from  the  falsehood  of  a 
Universal  or  truth  of  a  Particular,  we  can  know  the  char- 
acter only  of  the  Contradictory. 


166 


CONSPECTUS  OF  THE  DOCTRINE  OF 


JUDGMENTS,  considered 
in  reference  to 
Quantity,  are  either  Univer- 
sal or  Particular ;  to 
Quality,  are  either  Affirma- 
tive or  Negative ;  to 
Quantity  and  Quality,  are 
of  four  sorts :  — 


Affirmative  Predesignations  of  Univer. 
sal  Judgments. 

All  _  Every  —  Each—  This  —  That 
—  These  —  Those  —  a  Proper 
Name. 

A^    Universal  Affirmative. 

e.  g.  All  X  is  Y. 

All  metals  are  lustrous. 


IMMEDIATE   INFERENCE  proceeds 

BY    INFINITATION 

of  the  Terms  of  a  Judgment,  or  by  dropping  their  Infini- 
tation,  the  Judgments  thus  produced  being,  in  certain 
cases,  equipollent,  or  equivalent  to  those  from  which 
they  were  derived. 


by  Opposition, 

or  the  relation  that    A 
exists  betweenjudg- 
ments    which    have 
the  same  naked  or  | 
unquantified  Subject  J 
and   Predicate,   but  "° 
differ    in    Quantity, 
or  Quality,  or  both 


Z        Sab-Contrary. 


Four  Kinds 

1.  Contradiction 
exists    between    Judgments 
which  differ  both  in  Quan- 
tity and  Quality. 
Rule.  —  Contradictories  can- 
not both  be  true  and  cannot 
both  be  false.     Hence, 
to  posit  A  is  to  sublate  O 
«      E    «        "         I 
to  sublate  A  is  to  posit    O 
«  E     ■       "        I 

and  conversely, 

to  posit  O  is  to  sublate  A 


by  Conversion, 

or  causing  the  Subject  and 
Predicate  of  a  Judgment 
to  change  places  with  each 
other,  but  in  such  man- 
ner that  if  the  Convertend 
is  true,  then  the  Converse 
will  be  true  also. 


Three  Kinds 

1.  Simple,  E  &  I, 

without  changing  either  the  Quantity 

or  the  Quality.     (Ecce-tibi.) 
Convertend.    No  X  is  Y.  E  into 

Converse.       No  Y  is  X.  E. 

Convertend.    Some  X  are  Y.     I  into 
Converse.       Some  Y  are  X.     I. 


JUDGMENTS   AND   IMMEDIATE   INFERENCE. 


167 


Negative  Predesignations  of   Univer- 
sal Judgments. 

None  —  Not  any  —  Not  one  —  Not 
this  —  Not  that  —  "  Not "  prefixed 
or  suffixed  to  a  Proper  Name. 


Predesignations  of  Particular  Judg- 
ments, either  Affirmative  or  Nega- 
tive. 

Some  —  Not  all  —  or  any  indication 
of  an  indefinite  part  of  a  whole. 


E.  Universal  Negative. 

No  X  is  Y. 
No  quadruped  is  rational. 


I.  Particular  Affirmative. 

Some  X  are  Y. 
Some  swans  are  black. 


O-  Particular  Negative. 

Some  X  are  not  Y. 
Some  men  are  not  fa- 
mous. 


Two  Kinds  of  Infinitation. 


Rule.  —  To  change  the  Infinitation  of 
the  Predicate,  either  by  infinitating 
it  or  by  dropping  its  Infinitation, 
change  the  Quality  of  the  Judg- 
ment ;  the  Quantity  of  the  Judg- 
ment remains  unaltered. 


Rule.  —  To  change  the  Infinitation  of 
the  Subject,  convert  the  Judgment, 
and  then  either  change  the  Quality, 
or  change  the  Infinitation  of  the 
(old)  Predicate  also.  Here,  also, 
the  Quantity  is  unaltered. 


of  Opposition. 


3.  Contrariety 
between     Universal 
Judgments    that  differ  in 
Quality,  but    are   alike  in 
Quantity. 
Rule. —  Both  Contraries  may 
be   false,  but  both  cannot 
be  true.     Hence, 
to  posit  A  is  to  sublate  E 
E    »        «        A 


3.  SUB-CONTRARIETT 

exists  between  Particular 
Judgments  that  differ  in 
Quality,  but  are  alike  in 
Quantity. 

Rule. — Sub-Contraries  may 
both   be  true,  but  cannot 
both  be  false.    Hence, 
to  sublate   I   is  to  posit  O 

0       44  44  ! 


4.   StTBALTBBNATKm 

exists  between  Judgments 
alike  in  Quality,  but  differ- 
ent in  Quantity. 

Rule.  —  If  the  Subalternans 
(the  Universal)  is  true,  the 
Subalternate  (the  Particu- 
lar) is  also  true  •,  and  if  the 
Subalternate  is  false,  the 
Subalternans  is  false  also. 
Hence, 
to  posit  A  is  to  posit    I 

44  JJ  44  44  0 

to  sublate  I  is  to  sublate  A 
**         O    "        **       ■ 


of  Conversion.     (Hoc  capessit.*) 


2.  Per  Accidens,  A  &  E, 

changing  the  Quantity,  but  not  the 

Quality.     (Anni-geros.) 
Convertend.  All  X  is  Y.  A  into 

Converse.      Some  Y  is  X.        I. 
Convertend.  No  X  is  Y.  E  into 

Converse.      Some  Y  is  not  X.  O. 


3.  By  Contraposition,  A  &  0> 

changing,  not  the  Quantity,  but  the 
Quality,  through  infinitating  the 
Predicate.     (Ante-boni.) 

Convertend.  All  men  are  mortal.    A. 

Converse.      No  immortal  is  man.  E. 

Convertend.  Some    men    are    not 

white.  O- 

Converse.   Some  not-white  are  men.  L 


168 


THE   DOCTRINE   OF   IMMEDIATE   INFERENCE. 


Sub- Contrary 


That  the  various  points  in  the  doctrine  of  this  sort  of 
Immediate  Inference  might  be  more  easily  remembered. 

the  old  logicians  contrived, 
not  some  mnemonic  verses, 
as  on  other  occasions,  but 
the  accompanying  inge- 
nious diagram,  which  may 
be  called  the  Square  of 
Opposition.  It  is  very 
easy  to  retain  the  whole 
theory  in  the  memory, 
when  we  observe  the 
proper  position,  upon  this 
square,  of  the  vowels  which 
indicate  the  four  species  of  Judgments.  The  upper  line 
belongs  to  the  Universals,  A  and  E ;  the  lower  line  to  the 
Particulars,  I  and  O ;  the  left  hand  to  the  Affirmatives, 
A  and  I ;  and  the  right  to  the  Negatives,  E  and  O.  Then 
it  is  easily  remembered,  that  the  two  diagonals  represent 
Contradiction,  the  upper  line  Contrariety,  the  lower  one 
Sub-Contrariety,  and  each  of  the  two  sides  Subalternation. 
For  the  further  convenience  of  learners,  I  have  brought 
together  in  the  preceding  Conspectus  the  principal  techni- 
calities and  rules  in  the  Aristotelic  doctrine  of  Judgments 
and  Immediate  Inference. 

Hamilton  has  considerably  enlarged  and  modified  the 
doctrine  of  Immediate  Inference  by  Opposition,  by  intro- 
ducing, what  the  logicians  had  hitherto  neglected,  the 
semi-definite  meaning  of  some,  —  that  is,  some  at  most,  — 
some  excluding  all  and  none.  In  the  Aristotelic  doctrine, 
some  was  applied  exclusively  in  its  wholly  indefinite  mean- 
ing, as  some  at  least,  — some,  perhaps  all; —  and  in  nega- 
tives, some,  perhaps  none.  Yet,  as  Hamilton  remarks,  some 
is  always  thought  as  semi-definite  when  the  other  Term 
of  the  Judgment  is  Universal ;  and  it  is  only  when  both 


OPPOSITION  AND  INTEGRATION.  169 

Terms  are  Particular,  that  the  some  of  each  is  left  wholly- 
indefinite.  Thus,  when  we  say,  Some  men  are  (all)  black, 
we  mean  to  deny  that  all  are  black ;  Some  flowers  are  not 
(any)  fragrant,  denies  that  none  are  fragrant. 

But  in  the  case  of  Subalternation,  which  Hamilton  pre- 
fers to  call  Restriction,  if  we  introduce  this  semi-definite 
meaning,  and  think  some  as  some  only  —  not  all,  instead  of 
having  an  Inference  from  the  Subalternans  to  the  Subalter- 
nate,  we  find  a  true  Opposition  between  them;  to  adopt 
the  Hamiltonian  word,  the  two  Judgments  are  Incompos- 
sible.  Thus,  Some  (only  —  not  all)  men  are  yellow,  is  really 
opposed  to  All  men  are  yellow,  instead  of  being  an  Infer- 
ence from  it ;  and  in  like  manner,  Some  (not  all)  bipeds 
are  not  men,  is  opposed  to  No  bipeds  are  men.  This  new 
sort  of  Opposition  or  Incompossibility,  as  it  exists  between 
two  Judgments  which  are  alike  in  Quality,  either  both 
Affirmatives  or  both  Negatives,  while  the  other  two  sorts, 
Contradiction  and  Contrariety,  differ  in  Quality,  is  called 
Inconsistency.  Of  course,  as  two  Inconsistents,  like  any 
other  two  Incompossibles  or  Opposites,  cannot  both  be 
true,  the  true  Inference  is,  that  by  positing  either  A  or  I, 
E  or  O,  the  other  is  sublated.  To  express  the  whole  doc- 
trine of  Subalternation  or  Restriction  in  one  rule ;  —  If 
some  means  some  — perhaps  all,  the  Subalternate  is  a  direct 
Inference  from  positing  the  Subalternans ;  but  if  some 
means  some  —  not  all,  the  Subalternans  and  Subalternate 
are  Opposite  or  Incompossible,  so  that,  by  positing  either, 
the  other  is  sublated. 

Again,  it  has  already  been  shown  that  Sub-Contrariety 
is  properly  no  Opposition  at  all,  so  that  both  Judgments 
may  be  true  ;  though,  as  both  cannot  be  false,  sublating  one 
enables  us  to  posit  the  other.  But  if  we  introduce  the 
semi-definite  meaning  of  some  here  also,  we  have  a  new 
Inference  from  one  to  the  other ;  —  from  the  one  some, 
which  is  a  part,  to  the  other  some,  which  is  the  remaining 


170  THE  DOCTRINE   OF  IMMEDIATE  INFERENCE. 

part  necessary  to  constitute  the  whole.  This  sort  of  Infer- 
ence Hamilton  would  call  Integration,  as  its  effect  is,  after 
determining  one  part,  to  reconstitute  the  whole  by  bringing 
into  view  the  remaining  part.  Thus,  if  I  know  that  Some 
(not  all)  men  are  white,  I  can  immediately  infer  that  Some 
(other)  men  are  not  white;  and  if  Some  poets  are  not  philos- 
ophers, it  follows  that  Some  (other)  poets  are  philosophers. 
In  such  cases,  though  the  two  Judgments  are  different  in 
Quality,  they  are  not  opposed,  but  congruent ;  and  the 
Inference  may  be  not  only  to  all  others  definitely,  but  to 
some  others  indefinitely.  It  is  valid,  also,  whether  some 
appears  in  the  Subject  or  Predicate.  Thus,  from  Men  are 
some  animals,  we  immediately  infer  that  Men  are  not  some 
(other)  animals  (say,  brutes).  Here,  the  Inference  con- 
cerns the  Predicate,  while  in  the  preceding  cases  it  con- 
cerned the  Subject. 

To  apply  the  whole  doctrine  of  Incompossibility  and  In- 
tegration, in  both  meanings  of  the  word  some,  to  the  eight 
Hamiltonian  Judgments,  is  evidently  a  long  and  complex 
process.  The  following  table  (page  172),  in  which  the 
whole  process  is  worked  out,  is  borrowed  from  Sir  William 
Hamilton,  and  placed  here,  not,  of  course,  that  it  may  be 
committed  to  memory,  but  because  the  examination  of  it 
will  be  a  useful  exercise  for  the  learner.  In  explanation 
of  it,  observe  that  the  Incompossibility,  or  the  fact  that  the 
two  Judgments  cannot  both  be  true,  —  and  in  some  cases, 
the  Restriction  (Subalternation)  and  the  Integration, — 
may  be  bilateral  (here  marked  bi),  as  affecting  both  Subject 
and  Predicate  ;  thus, 

All  physical  laws  are  all  efficient  causes. 

Not  any  physical  law  is  any  efficient  cause. 
Or  unilateral  (u?i),  as  affecting  either  the  Subject  only 
thus, 

All  men  are  all  rational. 

Some  men  are  not  (any)  rational. 


OPPOSITION  AND  INTEGRATION.  171 

Or  the  Predicate  only ;  thus,  —  some  in  the  second  Judg- 
ment being  semi-definite,  — 

All  dogs  are  all  barking  animals. 

All  dogs  are  some  barking  animals. 
Or  it  may  be  unilateral  cross  (un.  cr.),  as  reversing  in 
the  one  Judgment  the  relation  of  Genus  and  Species  — 
containing  and  contained  —  which  exists  between  the 
Terms  of  the  other  Judgment ;  thus,  some  being  semi- 
definite, 

All  whites  are  some  civilized. 

Some  whites  are  all  civilized. 
Or  bilateral  cross  (hi.  er.),  as  affecting  both  Terms,  but  m 
opposite  relations,  —  as   from   Particular   to  Universal  in 
the  Subject,  and  from  Universal  to  Particular  in  the  Predi 
cate  ;  thus,  some  being  semi-definite, 

Some  blacks  are  all  Africans. 

Not  any  black  is  some  Africans. 
Or  bilateral  direct  (bi.  di.),  as  affecting  both  Terms,  and 
excluding  any  intermediate  or  third  Judgment,  both  propo- 
sitions remaining  the  same  after  conversion  ;  thus, 

Some  men  are  (some)  irrational. 

Not  any  man  is  (any)  irrational. 


>^  OP"  TRF,      * 


172 


THE   DOCTRINE   OF   IMMEDIATE   INFERENCE. 


TABLE 

op  the  Mutual  Relations   of   the  Eight  Propositional  Forms   o* 
either  System  of  Particularity.     (For  Generals  only.) 


1 

§ 

1 

if! 

o 

£ 

c 

g 

4 

.A  *> 

II 

Restr.  bi. 

Restr.  MM. 

Restr.  un. 

Restr.  it*. 

Restr.  un. 
Restr.  un. 

Res.  &  Int.  bi. 
Integr.  un. 
Res.  &  Int.  un. 

Integr.  un. 
Res.  &  Int.  un. 

Res.  &  Int.  un. 
Res.  &  Int.  un. 
Integr.  bi. 

.*g| 

?! 

p.  un. 
Restr.  un. 
Restr.  M. 

Restr.  un. 
Restr.  un. 

Restr.  un. 
Restr.  wn. 
Restr.  bi. 

Restr.  un. 
Restr.  un. 

-•2 

V] 

1—2 
1—3 
1—4 

2—4 
3—4 

6—6 

6—8 

6—8 
7-8 

1—8 
2—6 
2—8 

3—7 
3—8 

4_6,  6—4 
4—7,  7—4 
4—8,  8—4 

a 
o 

3 

c    £ 
s  ©"3 
cs 

I 

£5 

a* 

J* 

n 

Incons.  un. 
Incons.  un. 

Incons.  un.  cr. 

Incons.  un. 
Incons.  un. 

Doubtful,  cr. 

Contrar.  bi. 
Contrar.  un. 
Contrar.  un. 

Contrar.  un. 

Contrar.  bi.  cr. 

Contrar.  un. 
Contrar.  bi.  cr. 

Contrar.  bi.  di. 

1? 
•I 

H 

Doubtful,  cr. 

Contrar.  it*. 
Contrar.  un. 
Contrar.  un. 

Contrar.  un. 

Repugn,  it.  cr. 

Contrar.  un. 
Repugn,  bi.  cr. 

Repugn,  it*  di. 

•a 
•**S2 

pi 

"a 

> 

<i;Si:SS     <~a~=£     <<-£<<  =  -<<-  ~<i<~~1 
1  1  1   1  1  1      Mill      1   1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 
£  «2  «2  toes  ,4      bbcccJ     45  «8  45  «£  <e  Vo  «e«3  <±  *  «  je_ 

3!f 

5  E 

E  1   1   1   1   1   1  |c  i   1   1   1   1   1  ^  1   1   1   1   1   '   1   1   1   1   1   1   1   1   1   1 

3                                        _                         ^ 

Abbreviations-.    Contrar.  =  Contraries  ;  Incons.  =  Inconsistent*  ;  Int.  or  Integr.  =■  In. 
egration  ;   Repugn.  =  Repuynants,  Contradictories  ;   Res.  or  Restr.  =  Restriction,  Sub- 
alternation  ;  Blanks,  in  I  =  Compossibles  ;  in  II.  =  No  inference. 
This  Table  may  not  be  quite  accurate  in  details. 


OPPOSITION  AND  INTEGRATION.  173 

It  appears  from  this  Table,  that  Afi  and  Ina  (A  and  O), 
which,  on  the  Aristotelic  doctrine,  are  Contradictories,  be- 
come only  Contraries  when  we  admit  the  semi-definite 
meaning  of  some  ;  for  by  sublating  Ina,  which  denies  only 
a  part  (some  only),  we  know  not  whether  to  posit  Afi, 
which  affirms  the  whole,  or  Ifi,  which  affirms  only  some 
(other)  part,  or  Ana,  which  denies  the  whole  ;  since  each 
of  these  three  is  incompossible  with  Ina.  ■  For  the  same 
reason,  If  a  and  Ani,  which  are  only  A  and  O  converted, 
are  merely  Contraries  on  this  system,  though  Contra- 
dictories on  the  other,  wherein  some  means  perhaps  all. 
Indeed,  there  can  be  no  Contradiction  on  this  system, 
wherein  whole  and  part  negative  each  other,  just  as  much 
as  affirmation  and  negation.  The  only  Contradictories  are 
those  in  which  the  distinction  of  whole  and  part  does  not 
exist ;  —  Judgments  about  Singulars  or  Individuals,  for 
instance,  and  about  Universals  regarded  as  Singulars  or 
as  undivided  wholes.  Thus,  Common  salt  is  chloride  of 
sodium  contradicts  Common  salt  is  not  chloride  of  so- 
dium ;  for  Common  salt,  though  really  a  General  Term, 
is  here  actually  thought  as  undivided,  so  that  the  two 
Judgments  contradict  each  other  as  directly  as  do  these 
two  Singulars,  —  John  is  sick,  John  is  not  sick.  If  either 
Judgment  in  one  of  these  pairs  is  sublated,  the  other  is 
necessarily  posited. 

"The  propositional  form  Ifi  is  consistent  with  all  the 
affirmatives  ;  Ini  is  not  only  consistent  with  all  the  nega- 
tives, but  is  compossible  with  every  other  form  in  uni- 
versals. It  is  useful  only  to  divide  a  class,  and  is 
opposed  only  by  the  negation  of  divisibility." 

The  whole  scheme  of  Opposition  upon  this  system  may 
be  safely  characterized  as  too  complex  to  be  of  any  prac- 
tical use,  though  the  learner  may  be  profited  by  some 
stuly  of  its  details. 


174  MEDIATE  INFERENCE   OR  SYLLOGISM. 


CHAPTER    VII. 

THE    DOCTRINE    OF    MEDIATE    INFERENCE:     THE    ARISTOTELIO 
ANALYSIS  OF  SYLLOGISMS. 

1.  Figure  and  Mood.  —  2.  Conditional   Syllogisms.  —  3.  Defective  and 
Complex  Syllogisms. 

MEDIATE  Inference  is  that  act  of  Pure  Thought, 
whereby  the  relation  of  the  two  Terms  of  a  pos- 
sible Judgment  to  each  other  is  ascertained  by  comparing 
each  of  them  separately  with  a  third  Term.  Thus,  if  I 
cannot  immediately  determine  whether  A  is,  or  is  not,  B, 
I  can  compare  each  with  M.  If,  as  the  result  of  such  com- 
parison, it  is  found  that  A  is  M  and  B  is  M,  then  we  infer 
mediately  —  that  is,  through  this  relation  of  each  to  a  third 
—  that  A  is  B.  But  if  this  comparison  shows  that  one  of 
these  Terms  is,  and  the  other  is  not,  M,  then  we  infer 
mediately  that  A  is  not  B.  The  affirmative  conclusion  is 
evidently  governed  by  the  Axiom  of  Identity,  which  de- 
clares that  A  is  B,  if  it  is  that  (M)  which  is  the  equivalent 
of  B  ;  or  to  use  language  more  consonant  with  the  phrase- 
ology hitherto  employed,  and  converting  B  is  M'mto  Mis 
B,  we  say  that  B  is  a  Mark  of  A,  when  it  is  a  Mark  of 
that  (M)  which  is  a  Mark  of  A,  —  nota  notce  est  nota  rei 
ipsius.  The  negative  conclusion  results  from  the  Axiom 
of  Non-Contradiction,  which  declares  that  A  is  not  B,  when 
it  is  equivalent  to  that  (or  has  for  a  Mark  that)  (M), 
which  is  not  B ;  or,  what  is  the  same  thing,  when  it  is  not 
equivalent  to  that  (M)  which  is  B. 

The  fundamental  principle  of  Mediate  Inference  or  Syl- 


THE  ARISTOTELIC   ANALYSIS.  175 

logism  is  thus  traced  to  those  Axioms  which,  as  we  have 
already  seen,  must  govern  all  the  processes  of  Pure 
Thought ;  or  rather,  Mediate  Inference  itself  is  but  one  of 
the  special  applications  of  those  Axioms.  Instead  of  using 
these  Primary  Axioms  themselves,  logicians  have  usually, 
in  order  to  demonstrate  the  processes  of  syllogistic  reason- 
ing, preferred  to  employ  certain  intermediate  principles  or 
maxims,  one  of  which  we  have  just  mentioned,  —  that  the 
Mark  of  a  Mark  w  a  Mark  of  the  thing  itself.  But  as  these 
maxims  can  be  directly  deduced  from  the  original  Axioms, 
to  which,  indeed,  they  owe  all  their  validity,  it  seems  bet- 
ter to  test  the  legitimacy  of  each  step  by  a  reference  to  the 
primary,  rather  than  to  any  derivative,  principle. 

Thus  far,  A  and  B,  in  their  comparison  with  M,  have 
been  regarded  simply  as  undivided  wholes ;  but  it  is  evi- 
dent that  the  same  considerations  will  hold  good  if  we  sub- 
stitute, for  either  or  both  of  them,  all,  or  any  indefinite  part, 
of  a  divided  Universal.  Thus,  if  we  find  that  Some  A  are 
M,  and  Some  B  are  M,  we  are  compelled  to  conclude,  by 
the  Axiom  of  Identity,  that  Some  A  are  (some)  B ;  or, 
taking  a  negative  instance,  if  Some  A  are  M,  and  Not  any 
B  is  M,  then  we  infer  that  Some  A  are  not  (any)  B. 
Hence  we  see  the  correctness  of  the  derivative  or  inter- 
mediate principle  which  Sir  W.  Hamilton  enounces  as 
"  the  supreme  Canon  of  Categorical  Syllogisms,"  —  In  so 
far  as  two  Notions  (Concepts  or  Individuals),  either  both 
agree,  or,  one  agreeing,  the  other  does  not  agree,  with  a  com- 
mon third  Notion,  in  so  far  these  Notions  do  or  do  not 
agree  with  each  other.  But  if,  by  calling  it  "  supreme,"  he 
means  that  it  is  the  ultimate  and  original  Canon,  his  posi- 
tion may  be  doubted ;  for  it  is  evidently  a  compound 
statement,  embracing,  with  an  unimportant  change  of 
phraseology,  the  two  Primary  Axioms  of  Identity  and 
Non-Contradiction,  and  guarding  them  with  those  limita- 
tions under  wluVh  alone  are  they  ever  applicable. 


176  MEDIATE  INFERENCE   OR   SYLLOGISM. 

We  have  seen  that,  though  either  or  both  of  the  two 
Terms  be  quantified  Particularly,  the  Syllogism  still  holds 
good,  —  at  least,  to  the  extent  to  which  the  two  Terms 
are  quantified.  But  the  third  Term  must  be  taken  Uni- 
versally at  least  once  in  comparing  it  with  the  other 
Notions ;  otherwise,  we  have  no  security  that  these  others 
are  compared  with  the  same,  or  "  a  common,"  third  Term. 
Though  we  know,  for  instance,  that  A  is  some  M,  and  B 
is  same  M,  still  we  cannot  conclude  that  A  is  B  ;  for  the 
u  some  M  "  which  is  A  may  not  be  the  same  "  some  M  " 
which  is  B.  Though  Some  learned  men  are  pedants,  and 
Some  learned  men  are  wise,  it  does  not  follow  that  Pedants 
are  wise  ;  for  two  very  different  classes  of  learned  persons 
are  here  spoken  of.  Hence  we  have  this  general  rule  for 
all  Syllogisms,  that  the  Middle  Term  must  be  distributed 
(i.  e.  taken  Universally)  in  at  least  one  of  the  comparisons 
which  are  instituted  between  it  and  the  other  two  Terms. 
We  say,  "  at  least  one  "  of  the  two  comparisons ;  for  the 
other  may  be  quantified  Particularly  without  injury  to  the 
reasoning.  Thus,  if  All  men  are  mortal,  and  X,  Y,  and  Z 
are  (some)  men,  we  may  legitimately  conclude  that  X,  Y, 
and  Z  are  mortals  ;  for  to  whatever  class  these  "  some  men  " 
belong,  they  are  necessarily  included  under  "  all  men," 
who  are  declared  to  be  mortal. 

A  Syllogism  evidently  comprises  three  Judgments,  one 
of  which  affirms  the  agreement  or  non-agreement  of  its 
two  Terms  with  each  other  to  be  the  necessary  consequence 
of  two  other  Judgments,  in  which  a  common  third  Term 
is  affirmed  to  agree  with  both,  or  with  one  only,  of  these 
two  Terms.  The  main  Judgment  is  called  the  Conclusion  ; 
the  two  subsidiary  Judgments,  on  which  it  depends,  are 
termed  the  Premises;  and  the  necessary  connection  be- 
tween the  Premises  and  the  Conclusion  —  that  which 
entitles  us  to  infer  the  one  from  the  other  —  is  the  Con- 
sequence.    The  essence  of  the  Syllogism,  and  all  that  is 


THE  ARISTOTELIC  ANALYSIS.  177 

actually  affirmed  in  it,  is  this  necessary  consequence  of  the 
Conclusion  from  the  Premises.  Hence  the  Syllogism  is 
really  one,  —  a  single  and  indivisible  act  of  Thought. 
Though  apparently  complex  —  though,  in  a  certain  sense, 
including  three  Judgments  —  it  does  not  affirm  either  one 
of  them  taken  separately,  but  only  the  necessary  depend- 
ence of  one  upon  the  two  others.  Thus,  as  we  have  seen, 
both  Premises  may  be  false,  and  the  Conclusion  may  be 
false ;  and  yet  the  Syllogism  may  be  valid  or  correct  in 
Form,  for  the  latter  may  be  legitimately  deduced  from  the 
former.  The  following,  for  example,  is  a  valid  inference, 
though  each  of  the  Propositions  is  false. 

All  men  are  immortal , 

All  bipeds  are  men  ; 

Therefore,  all  bipeds  are  immortal. 
Hence,  in  order  to  dispute  or  deny  a  Syllogism  as  such,  we 
do  not  need  to  deny  either  of  its  three  Judgments,  but 
only  the  Consequence,  or  the  dependence  of  the  Conclu- 
sion upon  the  Premises  ;  in  other  words,  a  single  negation 
denies  all  that  the  Syllogism,  which  is  but  one  act  of 
Thought,  asserts.  We  say,  it  does  not  follow  that  A  is  B 
because  A  is  some  M  and  B  is  some  M ;  though  possibly 
A  is  B  for  some  other  reason. 

In  explanation  of  the  terms  employed  to  denote  the  pro- 
cess of  reasoning,  the  following  passage  is  borrowed  from 
Sir  William  Hamilton's  Lectures  on  Logic  :  "  Reasoning 
is  a  modification  from  the  French  raisonner  (and  this  is  a 
derivation  from  the  Latin  ratio)  and  corresponds  to  ratio- 
cinatio,  which  has,  indeed,  been  immediately  transferred 
into  our  language  under  the  form  ratiocination.  Ratiocina- 
tion denotes  properly  the  process,  but  improperly  also  the 
product,  of  reasoning ;  ratiocinium  marks  exclusively  the 
product.  The  original  meaning  of  ratio  was  computation^ 
and  from  the  calculation  of  numbers  it  was  transferred  to 
the   process  of  mediate  comparison  in  general.     Discourse 

8*  L 


178  MEDIATE  INFERENCE   OR  SYLLOGISM. 

(discursus,  SidvoLo)  indicates  the  operation  of  comparison, 
the  running  backwards  and  forwards  between  the  char- 
acters or  notes  of  objects ;  this  term  may  therefore  be 
properly  applied  to  the  Elaborative  Faculty  in  general 
[the  Understanding].  The  terms  discourse  and  discursus 
are,  however,  often,  nay  generally,  used  for  the  reasoning 
process  strictly  considered,  and  discursive  is  even  applied 
to  denote  Mediate,  in  opposition  to  Intuitive  [or  Imme- 
diate], judgment,  as  is  done  by  Milton. 

*  Whence  the  soul 
Reason  receives,  and  reason  is  her  being, 
Discursive  or  intuitive ;  discourse 
Is  oftest  yours/ 

The  compound  term,  discourse  of  reason,  unambiguously 
marks  its  employment  in  this  sense. 

'A  beast  that  wants  discourse  of  reason 
Would  have  mourned  longer.' 

Argumentation  is  derived  from  argumentari,  which  means 
argumentis  uti.  Argument  again  (argumentum)  —  what 
is  assumed  in  order  to  argue  something  —  is  properly  the ' 
middle  notion  in  a  reasoning,  —  that  through  which  the 
Conclusion  is  established.  It  is  often,  however,  applied 
as  coextensive  with  argumentation.  Inference  or  illation 
(from  infero)  indicates  the  carrying  out  into  the  last  Prop- 
osition what  was  virtually  contained  in  the  antecedent 
Judgments.  To  conclude  (concludere),  again,  signifies  the 
act  of  connecting  and  shutting  into  the  last  Proposition  the 
two  notions  which  stood  apart  in  the  two  first.  A  conclu- 
sion is  usually  taken,  in  its  strict  and  proper  signification, 
to  mean  the  last  Proposition  of  a  reasoning ;  it  is  some- 
times, however,  used  to  express  the  product  of  the  whole 
process.  To  syllogize  means  to  form  Syllogisms.  Syllogism 
(avWoyiapos)  seems  originally,  like  ratio,  to  have  denoted 
a  computation,  —  an  adding  up,  —  and,  like  the  greater  part 
of  the  technical  terms  in  Logic  in  general,  was  borrowed 


THE  ARISTOTELIC  ANALYSIS.  179 

by  Aristotle  from  the  mathematicians.  This  primary 
meaning  of  these  two  words  favors  the  theory  of  those 
philosophers  who,  like  Hcl  bes  and  Leidenfrost,  maintain 
that  all  Thought  is,  in  fact,  at  bottom,  only  a  calculation, 
a  reckoning.  2v\\oyicr/j,6$  may,  however,  be  considered 
as  expressing  only  what  the  composition  of  the  word  de- 
notes, —  a  collecting  together ;  for  avWoyl&crOat,  comes 
from  avWeyeiv,  which  signifies  to  collect.  Finally,  in 
Latin,  a  Syllogism  is  called  collection  and  to  reason,  colligere. 
This  refers  to  the  act  of  collecting,  in  the  Conclusion,  the 
two  notions  scattered  in  the  Premises." 

Thus  the  unifying  office  of  the  Understanding,  to  which 
we  have  before  adverted,  is  again  brought  to  view.  As  a 
Judgment  is  an  act  whereby  the  two  notions  which  are  its 
Terms  are  brought  together  into  one,  so  a  Syllogism  — 
Reasoning  proper  —  Mediate  Inference  —  is  that  act  of 
Pure  Thought  whereby  the  two  Judgments  which  are  its 
Premises  are  collected  and  summed  up  into  one  in  the 
Conclusion ;  or,  what  is  the  same  thing  expressed  in  relation 
to  the  Terms,  whereby  three  notions  are  reduced  to  unity. 

"Without  the  power  of  Reasoning,"  says  Hamilton, 
"we  should  have  been  limited  in  our  knowledge  (if 
knowledge  under  such  a  limitation  would  deserve  the 
name  of  knowledge  at  all)  —  I  say,  without  Reasoning, 
we  should  have  been  limited  to  a  knowledge  of  what  is 
given  by  Immediate  Intuition;  we  should  have  been 
unable  to  draw  any  inference  from  this  knowledge,  and 
have  been  shut  out  from  the  discovery  of  that  countless 
multitude  of  truths,  which,  though  of  high,  of  paramount 
importance,  are  not  self-evident.  This  faculty  is  likewise 
of  peculiar  utility,  in  order  to  protect  us  in  our  cogitations 
from  error  and  falsehood,  and  to  remove  these,  if  they 
have  already  crept  in.  For  every,  even  the  most  com- 
plex, web  of  thought  may  be  reduced  to  simple  Syllo- 
gisms ;  and  when  this  is  done,  their  truth  or  falsehood,  at 


180  MEDIATE  INFERENCE   OR   SYLLOGISM. 

least  ill  a  logical  relation,  flashes  into  view."  Hence,  as 
Dr.  Whately  remarks,  "the  Syllogistic  theory  does  not 
profess  to  furnish  a  peculiar  method  of  reasoning,  but  only 
to  set  forth  a  method  of  analyzing  that  mental  process  which 
must  invariably  take  place  in  all  correct  reasoning  "  ;  and 
again,  "  a  Syllogism  is  evidently  not  a  peculiar  kind  of 
argument,  but  only  a  peculiar  form  of  expression  in  which 
every  argument  may  be  stated." 

The  power  of  reasoning,  of  drawing  Mediate  Inferences, 
like  that  of  framing  Concepts,  is  at  once  a  proof  of  man's 
superiority  over  the  brutes,  and  of  his  inferiority  to  Ms 
Creator.  Brutes  cannot  reason,  nor  even  form  Judgments 
respecting  classes  of  things,  their  knowledge  being  con- 
fined, as  we  have  seen,  to  Intuitions,  —  to  Singulars.  On 
the  other  hand,  the  Infinite  Mind  knows  immediately  or 
intuitively  the  relation  of  one  thing  or  class  of  things  to  an- 
other, without  being  compelled  to  ascertain  indirectly  their 
agreement  or  non-agreement  through  their  relations  to  a 
third  or  Middle  Term.  The  power  of  Mediate  Inference  is 
a  help  for  an  imperfect  intellect ;  Omniscience  needs  no  help. 

The  brief  view  which  has  now  been  given  comprises  all 
the  essential  principles  of  Mediate  Inference,  —  that  is,  all 
the  rules  to  which  all  Syllogisms,  whatever  may  be  their 
peculiarities  in  other  respects,  must  conform.  They  may 
be  summed  up  as  follows  :  — 

1.  A  Syllogism  must  contain  three  Terms,  and  no  more  ; 
namely,  the  two  whose  agreement  or  disagreement  we  wish 
to  ascertain,  and  the  Third  or  Middle,  with  which  each  of 
these  is  separately  compared.  If  there  were  four  Terms, 
two  of  them  must  be  intermediate,  not  appearing  in  the  Con 
elusion ;  but  then  the  Premises  would  have  no  common  Term. 
If  we  know  only  that  A  is  M  and  B  is  iV",  we  have  no 
means  of  ascertaining  the  relation  of  A  and  B  to  each  other. 

2.  A  Syllogism  must  contain  three  Judgments,  and  no 
more  ;  namely,  the  two  in  which  each  of  the  Terms  of  the 


THE  ARISTOTELIC  ANALYSIS.  181 

Conclusion  is  compared  with  the  Middle  Term,  and  that  m 
which  these  two  are  compared  with  each  other. 

3.  The  Middle  Term  must  be  distributed  (taken  univer- 
sally') in  at  least  one  of  the  Premises.  The  necessity  of 
this  Rule  arises,  as  we  have  seen,  from  the  fact  that  the 
two  Extremes,  in  order  to  be  compared  with  each  other, 
must  have  been  separately  compared  with  the  same  com* 
mon  Middle.  If  we  consider  no  other  kinds  of  Quantity 
than  all  and  some  (Universal  and  Particular),  the  Rule  as 
here  expressed  is  sufficient.  '  But  if  we  take  into  more 
definite  view  the  Quantity  of  some,  —  namely,  whether  it 
does  or  does  not  exceed  one  half,  —  the  Rule  may  be  made 
seemingly  less  stringent.  It  is  enough  that  the  quantifica- 
tions of  the  Middle  Term  in  both  Premises,  added  together, 
should  exceed  unity,  —  that  is,  exceed  its  possible  totality 
or  its  distribution  in  any  one  ;  for  the  amount  of  such 
excess  over  unity  then  constitutes  a  common  Middle  Term. 
Something  more  than  all  the  Middle  Term  has  been  men- 
tioned  in  the  Premises ;  and  both  Terms  in  the  Conclusion 
must  have  this  excess  as  a  common  element.  If  A  is  three 
fourths  of  M,  and  B  is  one  half  of  M,  then  at  least  one 
fourth  of  M  is  common  to  A  and  B  ;  and  their  agreement 
with  this  common  term  is  enough  to  insure  their  agreement 
with  each  other.  This  is  called  by  Hamilton  the  ultra-total 
quantification  of  the  Middle  Term.  It  deserves  mention,  but 
as  it  is  of  very  infrequent  use,  the  Rule  as  first  enounced 
for  the  quantification  of  the  Middle  is  practically  sufficient. 

4.  One  Premise  at  least  must  be  affirmative  ;  for  if  both 
Premises  are  negative,  the  Middle  Term  agrees  with 
neither  of  the  two  others,  and  therefore  affords  no  ground 
for  any  Inference  as  to  their  agreement  or  non-agreement 
with  each  other.  Though  we  know  that  A  is  not  iff  and 
B  is  not  M,  we  do  not  thereby  know  whether  A  is  or  is  not 
B.  A  good  general  is  not  a  coward,  and  Pompey  was  not 
a  coward ;  but  these  two  assertions  furnish  no  reason  for  be- 
lieving that  Pompey  either  was,  or  was  not,  a  good  general. 


182  MEDIATE  INFERENCE   OR   SYLLOGISM. 

5.  If  either  Premise  is  negative,  the  Conclusion  is  nega* 
tive  ;  for  as  one  Premise,  according  to  the  preceding  Rule, 
must  be  affirmative,  if  the  other  Premise  is  negative,  there 
is  a  difference  in  the  relation  of  the  two  principal  Terms  to 
the  Middle  Term,  and  hence  a  non-agreement  between  the 
two  Terms  themselves. 

6.  Neither  Term  must  be  distributed  in  the  Conclusion  if 
it  was  not  distributed  in  the  Premise;  for  if  only  some  is 
premised,  we  cannot  conclude  all. 

Logicians  have  usually  added  two  other  Rules,  that  the 
Conclusion  follows  the  weaker  part,  a  Negative  being  re- 
garded as  weaker  than  an  Affirmative,  and  a  Particular  as 
weaker  than  a  Universal ;  and  that  no  Conclusion  can  be 
drawn  from  two  Particular  Premises.  But  both  of  these 
result  only  from  a  combination  of  Rules  5  and  6  with  3  ; 
hence  they  hardly  need  to  be  considered  here,  but  I  ap- 
pend a  demonstration  of  them  in  the  note.*    No  syllogism 

*  As  the  two  additional  Rules  were  constructed  with  special  reference  to 
the  Aristotelic  doctrine  of  Judgments,  they  can  be  conveniently  demon- 
strated only  by  bearing  in  mind  the  following  maxims,  which  have  already 
been  laid  down  in  the  exposition  of  that  doctrine. 

1.  By  Subalternation,  Particular  Judgments  are  included  under  their 
corresponding  Universals  ;  that  is,  if  A  is  true,  I  is  also  true ;  and  the 
same  holds  good  of  E  and  O. 

2.  The  Subject  of  a  Judgment,  taken  universally  or  particularly,  is  that 
which  renders  the  Judgment  itself  Universal  or  Particular. 

3.  The  Predicate  of  an  Affirmative  Judgment  is  always  considered  as 
Particular. 

4.  The  Predicate  of  a  Negative  Judgment  is  always  regarded  as  Unive», 
sal,  —  that  is,  as  distributed. 

Now  there  "rust  always  be  in  the  Premises  one  more  Term  distributed  than  in 
the  Conclusion ;  for  by  Rule  3,  the  Middle  Term  (which  does  not  appear  in 
the  Conclusion)  must  be  distributed  in  at  least  one  of  the  Premises ;  and 
by  Rule  6,  if  any  Term  is  distributed  which  does  appear  in  the  Conclu- 
sion, it  must  also  be  distributed  in  the  Premises.  Then  it  follows  that  no 
Conclusion  can  be  drawn  from  two  Particular  Premises.  For  if  these  are  I 
and  I,  as  neither  Subject  nor  Predicate  of  I  is  Universal,  the  Middle  Term 
is  not  distributed.     If  they  are  I  and  O,  then,  by  Rule  5,  the  Conclusion  is 


THE  ARISTOTELIC  ANALYSIS.  183 

can  be  invalid  which  does  not  violate  one  or  more  of  the 
six  Rules  first  enounced. 

After  the  usual  manner  of  logicians,  the  foregoing  Rules 
have  been  summed  up  in  these  mnemonic  hexameters :  — 

Distribuas  medium,  nee  quartus  terminus  adsit; 
Utraque  nee  prsemissa  negans,  nee  particularis ; 
Sectetur  partem  conHusio  dcteriorem, 
Et  non  distribuat  nisi  cum  prsemissa,  negetve. 

♦  But  the  application  of  these  rules  may  become  a  matter 
of  considerable  complexity,  when  it  is  considered  that,  from 
the  same  naked  (unquantified)  Terms,  a  great  variety 
of  different  Syllogisms  may  be  formed.  Each  of  the  three 
Terms  may  be  either  Particular  or  Universal ;  each  of  the 
three  Judgments,  either  Affirmative  or  Negative  ;  the  Judg- 
ments may  be  placed  in  any  order  with  respect  to  each 

negative ;  then  its  Predicate  is  distributed ;  and  Rule  6,  taken  in  conjunc- 
tion with  what  has  just  been  stated  respecting  the  number  of  distributed 
Terms  in  the  Premises,  requires  one  of  these  Premises  to  be  Universal. 

Again,  if  either  Premise  is  Particular,  the,  Conclusion  must  be  Particular. 
For  the  Subject  of  a  Universal  Affirmative  Conclusion  must  be  Universal ; 
therefore,  in  the  Premise  wherein  this  Subject  appears,  it  must,  by  Rule  6, 
be  Universal,  and  the  Middle  Term,  which  is  therein  joined  with  it,  must 
consequently  be  Particular,  since  it  must  be  the  Predicate  of  an  Affirmative 
Judgment.  Then  the  Middle  Term,  in  order  to  be  once  distributed,  must 
be  the  Universal  Subject  of  the  other  Premise.  Hence,  if  the  Conclusion  is 
Universal  Affirmative,  both  Premises  must  be  Universal. 

And  if  the  Conclusion  is  Universal  Negative,  both  Premises  must  also  be 
Universal.  For  both  Terms  of  the  Conclusion  are  then  distributed ;  and  as 
the  Middle  Term  must  also  be  distributed,  there  must  be  at  least  threo 
Terms  distributed  in  the  Premises.  But  this  cannot  be,  unless  both  Prem- 
ises are  Universal,  since  both  of  them,  by  Rule  4,  cannot  be  Negative. 
Hence,  whether  the  Conclusion  is  Affirmative  or  Negative,  if  it  be  Univer- 
sal, both  Premises  must  be  Universal.  Then,  if  either  Premise  is  Particular, 
the  Conclusion  must  be  Particular. 

But  according  to  Rule  5,  if  either  Premise  is  Negative,  the  Conclusion 
is  Negative.  Then,  the  Conclusion  must  follow  the  weaker  part ;  —  that  is,  it 
must  be  Particular,  if  either  Premise  is  Particular,  and  Negative,  if  either 
Premise  is  Negative.  —  Q.  E.  D. 


184  MEDIATE  INFERENCE   OR  SYLLOGISM. 

other,  and  for  three  Judgments,  six  different  orders  of  posi- 
tion are  possible ;  and  each  of  the  three  Terms  may  be 
either  Subject  or  Predicate  in  either  or  both  of  the  Prem- 
ises, the  two  principal  Terms  also  assuming  either  place  in 
the  Conclusion.  The  larger  portion  of  the  numerous  Syl- 
logisms thus  formed,  it  is  true,  are  invalid,  as  offending 
against  one  or  more  of  the  preceding  Rules.  We  need 
some  more  succinct  mode  than  that  of  severally  applying 
to  ca?h  Syllogism  all  these  Rules,  before  we  can  be  satisfied 
that  it  is  impeccable.  Many  of  these  Syllogistic  forms, 
moreover,  are  equivalents  of  each  other;  that  is,  the  Rea- 
soning may  be  changed  from  one  form  to  another,  with- 
out impairing  its  validity,  or  even  changing  its  signification 
in  any  essential  respect.  But  of  these  equivalent  forms 
some  are  more  natural  and  obvious  than  the  others  ;  the 
mind  seeks  for  these  by  preference  ;  and  when  the  process 
of  reasoning  appears  in  one  of  these  natural  and  preferred 
forms,  its  validity  is  determined  with  ease  and  in  a  mo- 
ment. The  application  of  the  Rules  to  such  cases  is  made 
with  the  quickness  of  instinct,  and  may  be  reduced  almost 
to  a  mechanical  process. 

A  highly  ingenious,  though  artificial,  system  has  been 
contrived  of  classifying  these  numerous  Syllogistic  forms 
under  a  few  heads,  throwing  out  at  once  all  that  are  ille- 
gitimate, immediately  recognizing  the  remainder,  and  then 
transmuting  those  which  are  valid  in  substance,  but  un 
natural  and  obscure  in  form,  into  the  easy  and  familiar 
types  in  which  the  mind  quickly  perceives  their  legitimacy. 
The  study  of  this  system,  a  ready  use  of  which  may  be 
said  to  constitute  the  art  of  Syllogizing,  is  facilitated  by  a 
series  of  mnemonic  contrivances,  many  of  them  of  mar- 
vellous ingenuity  and  completeness.  The  notation  and 
most  of  the  operations  are  of  an  algebraic  character ;  and 
attempts  have  not  been  wanting  of  late  years  to  enlarge 
and  perfect  the  system  by  a  further  introduction  of  mathe- 


THE  ARISTOTELIC  ANALYSIS.  185 

matical  signs  and  processes.  The  failure  of  such  an  under- 
taking is  not  to  be  wondered  at,  for  it  proceeds,  as  it  seems 
to  me,  upon  a  mistaken  opinion  as  to  the  relative  position 
of  the  two  sciences.  Logic  is  not  a  department  of  mathe- 
matics. Rather  the  reverse  is  true.  Mathematics  is  the 
science  of  pure  quantity,  —  of  reasoning  about  dimensions 
and  numbers  in  the  abstract,  or  as  unmodified  by  any  of 
the  differences  of  quality  by  which  all  the  objects  of  thought 
are  actually  distinguished ;  and  it  is,  therefore,  only  a  de- 
partment, or  a  special  application,  of  the  far  more  compre- 
hensive science  which  has  for  its  object  Reasoning  itself 
and  all  its  subsidiary  processes,  and  thus  covers  the  whole 
domain  of  Pure  Thought.  All  computation  is  reasoning ; 
but  all  reasoning  is  not  computation,  and  therefore  cannot 
be  carried  on  by  the  processes,  or  be  made  subject  to  the 
special  laws,  of  pure  mathematics. 

Syllogistic  forms  are  classified  with  respect  to  Mood  and 
Figure,  the  former  having  regard  to  the  value  of  the  three 
component  Judgments,  and  the  latter  to  the  relative  posi- 
tion of  the  three  Terms  in  these  Judgments.     It  will  be 
convenient,  then,  to  have  a  uniform  mode  of  designating 
these  three  Terms.     In  future,  S  will  stand  for  the  Sub- 
ject, and  P  for  the  Predicate,  of  the  Conclusion,  and  M  for 
the  Middle  Term.     The  Consequence,  or  what  we  usually 
express  by  the  words  therefore,  consequently,  &c,  will  be 
indicated  by  three  dots  placed  thus  .\     For  example  :  — 
Mis  P; 
S  is  M; 
.\  S  is  P. 

To  facilitate  reference,  the  Logicians  have  given  special 
names  to  these  several  Terms  and  Judgments.  The 
Predicate  of  the  Conclusion  is  called  the  Major  Term,  and 
its  Subject  the  Minor  Term.  The  Premise  in  which  the 
Major  is  compared  with  the  Middle  Term  is  called  the 
Major  Premise,  and  that  in  which  the  Minor  is  compared 


L86  MEDIATE   INFERENCE   OR  SYLLOGISM 

with  the  Middle,  is  the  Minor  Premise.  These  names 
have  reference  to  the  Quantity  of  Extension  only,  and  are 
founded  upon  the  received  doctrine,  that  the  natural  order 
of  predication  is  that  in  which  the  Genus  is  predicated  of  the 
Species,  the  Species  of  the  Individual,  and,  generally,  the 
Extensive  whole  of  its  part.  Then  the  more  Extensive 
Term,  the  Major,  usually  occupies,  at  least  in  Affirmative 
Judgments,  the  Predicate's  place.  "  This,"  says  Dr. 
Thomson,  "  is  the  natural,  though  not  invariable,  order ; 
and  it  is  worthy  of  remark,  that,  even  in  Negative  Judg- 
ments, where,  from  the  negation,  the  two  Terms  cannot  be 
set  together  to  determine  their  respective  Extension,  if, 
apart  from  the  Judgment,  we  know  that  the  one  is  a  small 
and  the  other  a  large  class,  —  the  one  a  clearly  determined 
and  the  other  a  vague  notion,  —  we  naturally  take  the 
small  and  clearly  determined  Concept  for  the  Subject. 
Thus,  it  is  more  natural  to  say  that  the  Apostles  are  not 
deceivers,  than  that  No  deceivers  are  Apostles.  So  that,  if 
our  minds  are  not  influenced  loj  some  previous  thought  to 
give  greater  prominence  to  the  wider  notion,  and  so  make 
it  the  Subject,"  thus  reversing  the  primary  and  natural 
order,  the  Term  of  major  Extension  will  always  be  the 
Predicate,  and  that  of  minor  Extension,  the  Subject. 

As  these  names  —  Major,  Middle,  and  Minor  —  thus 
correctly  indicate  the  comparative  Extension  of  the  three 
Terms,  an  Affirmative  Syllogism  in  which  these  Terms 
occupy  their  natural  place  is  conveniently  symbolized  by 
three  concentric  circles,  of  which  the  outermost  and  largest 
indicates  the  Predicate  of  the  Conclusion,  or  the  Major 
Term ;  the  innermost  and  smallest,  the  Subject  of  the  Con- 
clusion, or  the  Minor;  and  the  intermediate  one,  the 
Middle  Term.     Thus:  — 

All  mammals  are  viviparous ;         All  M  are  P. 

All  whales  are  mammals ;  All  S  are  M. 

AH  whales  are  viviparous.  .*.  All  S  are  P. 


THE  ARISTOTELIC  ANALYSIS.  187 

Here  the  reasoning  is,  that  $,  which  is  a  part  of  M, 
must  also  be  a  part  of  P,  since  M  is  a  part  of  P.  "We  are 
thus  led  to  another  mode  of  enunciating  the  governing 
principle  of  all  Syllogisms,  that  a  part  of  a  part  is  a  part 
of  the  whole  ;  or,  as  Leibnitz  expresses  it,  contentum  contenti 
est  contentum  continentis.  This  principle  agrees  in  every 
essential  respect  with  the  famous  Dictum  of  Aristotle, 
usually  called  the  Dictum  de  omni  et  nullo,  that  whatever  is 
predicated  (affirmed  or  denied)  universally  of  any  Class 
(i.  e.  of  any  whole),  may  be  also  predicated  of  any  part  of  that 
Class.  Both  principles  have  been  already  recognized  and 
applied  in  the  doctrine  of  Subalternation.  The  name  of 
this  Dictum  is  derived  from  the  two  forms  which  it  assumes 
as  applied  either  to  affirmative  or  negative  Conclusions  ; 
the  Dictum  de  omni  being  thus  expressed,  Quicquid  de 
omni  valet,  valet  etiam  de  quibusdam  et  singulis ;  and  the 
Dictum  de  nullo  being,  Quicquid  de  nullo  valet,  nee  de  qui- 
busdam nee  de  singulis  valet.  Both  of  these  principles  are 
evidently  of  a  secondary  or  derivative  character,  their  af- 
firmative and  negative  forms  being  grounded  respectively 
upon  the  two  Axioms  of  Identity  and  Non-Contradiction  ; 
for  as  a  whole  is  identical  with  the  sum  of  all  its  parts, 
whatever  is  affirmed  •  or  denied  (distributively)  of  the 
whole  is  thereby  affirmed  or  denied  of  each  of  its  parts. 
Burgersdyck  remarks,  that,  for  the  purpose  of  applying  the 
Dictum  to  Syllogisms,  it  may  more  conveniently  be  thus 
expressed :  Whatever  Predicate  is  universally  affirmed  or 
denied  of  any  Middle  Term  or  Part  is  also  affirmed  or  de- 
nied of  any  Subject  which  is  contained  under  that  inter- 
mediate Term  or  Part. 

The  mode  of  symbolizing  the  mutual  relations  of  the 
three  Terms  of  a  Syllogism,  which  is  applied  above  to  a 
Universal  Affirmative,  may  be  extended  to  Negatives  and 
Particulars.  The  total  disagreement  of  two  Terms  with 
each  other,  which  is  expressed  by  a  Negative  Judgment,  is 


188  MEDIATE   INFERENCE   OR   SYLLOGISM. 

properly  indicated  by  two  Circles  which  do  not  coincide  in 
any  part.     Thus  :  — 


No  M  is  P  ; 

All  S  is  M ; 
■.  No  S  is  P. 


Both  the  partial  agreement,  and  the  partial  disagreement, 
of  two  Terms,  —  as  these  are  merely  two  aspects  of  one 

and  the  same  Thought, — 
are  properly  indicated  by 
the  same  symbol,  namely, 
two  circles  which  intersect. 
Some  S  are  M,  and  Some 
S  are  not  M,  are  both  ex- 
pressed by  this  symbol. 
Excepting  this  ambiguity, 
all  Syllogisms  can  be  adequately  symbolized  by  some  com- 
bination of  the  preceding  diagrams. 

Hitherto  we  have  regarded  the  Syllogism  only  as  a 
means  of  evincing  the  relation  of  two  Terms  to  each  other 
through  the  relation  of  each  to  a  common  or  Third  Term, 
But  the  Dictum  as  expressed  by  Burgersdyck  indicates 
another  aspect  of  the  Syllogism,  equivalent  indeed  to  the 
former  one,  but  in  certain  respects  more  convenient  for 
use.  The  Judgment  in  which  "  a  Predicate  is  universally 
affirmed  or  denied  of  any  Middle  Term  or  Part "  is  a  Gen- 
eral Rule ;  the  Judgment  that  a  given  "  Subject  is  con- 
tained under  that  intermediate  Term  or  part,"  is  the  Sub- 
sumption  of  this  Subject  under  the  condition  of  that  Rule ; 
and  then  the  Conclusion  following,  that  the  given  Subject  is 
governed  by  that  Rule,  is  a  solution  of  'the  doubt  with  which 
we  commenced,  whether  S  is,  or  is  ixut,  P.    Every  Syllogism, 


THE  ARISTOTELIC  ANALYSIS.  189 

then,  must  consist  of  three  Judgments,  one  of  which  must 
be  a  General  Rule,  or,  as  Hamilton  expresses  it,  a  Sump- 
tion ;  another  must  be  the  Subsumption  of  a  certain  Sub- 
ject under  that  Rule ;  and  the  third  is  the  Conclusion, 
that  this  Subject  is  determined  by  the  Rule.     Thus  :  — 

Sumption.  No  one  who  is  content  is  miserable  ; 

Subsumption.     Some  of  the  poor  are  content ; 

Conclusion.        Some  of  the  poor  are  not  miserable. 

It  is  not  difficult  to  prove,  say  the  Port  Royal  logicians, 
that  all  the  Rules  which  we  have  given  serve  only  to  show 
that  the  Conclusion  is  contained  under  (or  embraced  in  the 
Extension  of)  one  of  the  Premises,  which  is  a  General 
Rule  or  Sumption,  and  that  the  other  Premise,  the  Sub- 
sumption, shows  this ;  and  that  arguments  are  vicious  only 
when  they  fail  to  observe  this  method,  and  are  always  good 
when  it  is  observed. 

Kant  expresses  the  general  law  of  the  Syllogism,  as  thus 
conceived,  in  the  following  formula:  Whatever  stands 
under  the  condition  of  a  Rule,  that  stands  also  under  the 
Rule  itself.  As  the  former  view  regards  chiefly  the  three 
Terms,  so  this  one  has  primary  reference  to  the  three 
Judgments,  of  which  every  Syllogism  is  composed.  The 
former  view  does  not  contradict  the  latter ;  they  are  only 
two  aspects  of  the  same  thing.  But  what  we  have  hitherto 
termed  the  Major  Premise,  though  it  is  usually  the  same 
Judgment  that  is  here  called  the  Sumption,  is  not  always 
so.  Thus,  in  the  following  Syllogism,  (called  by  the 
Logicians  Disamis  of  the  Third  Figure,)  the  first  Judg- 
ment, as  it  contains  the  Predicate  of  the  Conclusion,  is  the 
Major  Premise  ;  but  the  second  Judgment  is  the  Sumption. 
Some  wicked  persons  are  men  of  high  rank ; 
All  the  wicked  are  miserable. 
.*.  Some  miserable  persons  are  men  of  high  rank. 

As  it  has  been  demonstrated  that  from  two  Particulars  no 
Conclusion  can  be  drawn,  every  Syllogism  must  have  for  a 


190 


MEDIATE   INFERENCE   OR   SYLLOGISM. 


Premise  at  least  one  Universal  Judgment ;  that  is,  one  of 
its  Premises  must  be  a  Sumption  or  General  Rule.  In  the 
First  Figure,  which  is  the  only  natural  and  obvious  form 
of  reasoning,  and  to  which  all  the  other  forms  can  be  re- 
duced, the  Sumption  is  always  the  Major  Premise. 


1.     Figure  and  Mood. 

The  Figure  of  a  Syllogism  depends  upon  the  relative 
position  of  its  three  Terms,  and  is  determined  by  the  posi- 
tion of  the  Middle  Term  in  the  Premises.  Now  the  Mid- 
dle Term  may  be  either  the  Subject  of  the  Major  Premise, 
and  the  Predicate  of  the  Minor,  in  which  case  we  say  the 
Syllogism  is  of  the  First  Figure  ;  or  it  may  be  the  Predi- 
cate of  both,  which  is  the  Second  Figure  ;  or  it  may  be  the 
Subject  of  both,  thus  constituting  the  Third  Figure ;  or  it 
may  be  the  Predicate  of  the  Major  and  the  Subject  of  the 
Minor,  thus  converting  the  First,  and  giving  rise  to  the 
Fourth  Figure.  Accordingly,  the  four  Figures  are  thus 
indicated. 


I. 

n. 

m. 

IV. 

MP 

PM 

MP 

PM 

SM 

SM 

MS 

MS 

SP 

.-.  SP 

.-.SP 

/.SP 

They  are  also  indicated  in  the  following  mnemonic 
line :  — 

Sub  prce  ;  turn  proe  prce  ;  turn  sub  sub  ;   turn  prce  sub. 

The  line  should  be  read  thus  :  —  The  Middle  Term  is,  first, 
Subject,  Predicate  ;  then,  Predicate,  Predicate ;  then,  Sid>- 
ject,  Subject;  lastly,  Predicate,  Abject. 

The  Fourth  Figure  is  not  recognized  by  Aristotle,  but  is 
accepted,  if  at  all,  on  the  supposed  authority  of  Galen. 
Most  modern  logicians  reject  it,  not  as  invalid,  but  as  un- 
natural and  unnecessary.     As  we  have  already  said,  the 


FIGURE   AND   MOOD.  191 

natural  order  of  predication  is  that  in  which  the  Genus  is 
predicated  of  the  Species,  or  the  more  Extensive  of  the  less 
Extensive  Term.  Then  it  follows  that  the  First  is  the 
only  natural  and  obvious  Figure,  as  it  is  the  only  one 
which  observes  this  order  throughout.  Here,  the  Predicate 
of  the  Conclusion,  which  is  the  Term  of  widest  Extension, 
appears  as  the  Predicate  of  the  Major  Premise ;  and  the 
Subject  of  the  Conclusion,  being  the  Term  of  least  Exten- 
sion, is  the  Subject  of  the  Minor  Premise,  —  the  Middle 
Term  appearing,  as  it  ought,  intermediate  between  the 
two,  being  of  less  Extension  than  P,  and  greater  than  S. 
Here  also,  as  Dr.  Thomson  remarks,  the  Conclusion  in  no 
way  disturbs  the  order  of  Terms  which  was  first  established 
in  the  Premises ;  for  the  Subject  of  the  Conclusion  appears 
also  as  a  Subject  in  the  Premises,  and  the  Predicate  as  a 
Predicate  ;  —  that  is,  no  Thought  which  was  primary  be- 
comes secondary,  nor  any  secondary  primary.  Take,  for 
instance,  the  following  Syllogism  in  the  First  Figure :  — 

1.  No  boaster  deserves  respect ; 
Some  heroes  are  (some)  boasters  ; 

,\  Some  heroes  do  not  deserve  respect. 

Here,  everything  is  in  its  natural  place  ;  each  Subject  is  of 
less  Extension  than  its  Predicate,  and  the  Terms  preserve 
the  same  relative  places  in  the  Conclusion  which  they 
occupied  in  the  Premises. 

But  change  this  Syllogism  into  the  Second  Figure,  by 
converting  the  Major  Premise,  thus :  — 

2.  No  person  deserving  respect  is  a  boaster ; 
Some  heroes  are  (some)  boasters ;         *■ 

.\  Some  heroes  do  not  deserve  respect. 

Here,  the  natural  order  is  violated  in  one  half  of  the  rea- 
soning ;  for  the  Subject  of  the  Major  is  the.  Predicate  of 
the  Conclusion,  and  has  wider  Extension  than  its  own 
Predicate. 


192  MEDIATE   INFERENCE   OR   SYLLOGISM. 

Again,  change  the  same  Syllogism  into  the  Third  Fig- 
lire,  by  converting  the  Minor  Premise,  thus  :  — 

3.  No  boaster  deserves  respect ; 
Some  boasters  are  (some)  heroes ; 

.\  Some  heroes  do  not  deserve  respect. 
Here,  the   other  half  of  the  reasoning  appears  unnatural 
and  forced.     The  Predicate  of  the  Minor  Premise  becomes 
the  Subject  of  the  Conclusion,   and  is  of  less  Extension 
than  its  own  Subject. 

To  change  this  Syllogism  into  the   Fourth  Figure,  we 
must  convert  both  Premises,  thus :  — 

4.  No  person  deserving  respect  is  a  boaster ; 
Some  boasters  are  (some)  heroes ; 

.*.  Some  heroes  do  not  deserve  respect. 
Here,  both  halves  of  the  reasoning  are  contorted,  so  that  it 
appears  wholly  unnatural.  Not  only  is  the  Predicate  of 
the  Minor  the  Subject  of  the  Conclusion  and  of  less  Extent 
than  its  own  Subject,  but  the  Subject  of  the  Major  is  the 
Predicate  of  the  Conclusion,  and  of  greater  Extent  than  its 
own  Predicate.  The  mind  revolts  at  this  perversion  ; 
striving  to  preserve  the  same  order  in  the  Conclusion 
which  it  observed  in  the  Premises,  the  Conclusion  which  it 
would  naturally  draw  from  these  two  Premises  is  this :  — 

No  person  deserving  respect  is  (some)  hero. 
Now,  this  Conclusion,  which  is  natural  and  obvious,  is  the 
Converse  of  the  former  one,  which  was  unnatural ;  and  it 
reduces  the  Syllogism  (changing  the  order  of  the  Premises) 
from  the  Fourth  to  the  First  Figure.  Hence  it  appears, 
that  what  is  called  the  Fourth  Figure  is  only  the  First 
with  a  converted  Conclusion ;  that  is,  we  do  not  actually 
reason  in  the  Fourth,  but  only  in  the  First,  and  then,  if 
occasion  requires,  convert  the  Conclusion  of  the  First. 
The  reasoning  is  indirect,  or  Mediate  in  a  double  sense; 
the  nominal  Conclusion  of  the  Fourth  is  actually,  but  in- 


FIGURE  AND  MOOD.  193 

directly,  obtained  by  converting  the  Conclusion  of  the 
First.  Hence,  many  Logicians  exclude  the  Fourth  alto- 
gether, and  call  those  Syllogistic  forms  which  would  other- 
wise fall  under  it  "  indirect  Moods  of  the  First  Figure." 
But  we  can  also  obtain,  if  we  see  fit,  indirect  Moods  from 
the  Second  or  Third  Figure,  by  converting  their  Conclu- 
sions also.  There  is  no  reason,  then,  for  giving  a  special 
class  of  these  "  indirect  Moods  "  to  the  First  Figure,  any 
more  than  to  the  Second  or  Third ;  that  is,  there  is  no 
reason  for  considering  the  Moods  of  the  so-called  Fourth 
Figure  at  all.  It  is  not  only  unnatural,  but  wholly  un- 
necessary. We  need  only  state,  that,  after  obtaining  tho 
ordinary  mediate  Conclusions  from  either  of  the  three  Fig- 
ures, we  may,  if  occasion  requires,  obtain  a  second  set  of 
Conclusions  immediately,  by  converting  the  former  ones. 

But  we  observe,  secondly,  that  the  natural  but  unex- 
pressed Conclusion  of  the  so-called  Fourth,  — 

"  No  person  deserving  respect  is  (some)  hero,"  — 
is  a  shocking  one  for  the  Aristotelians,  for  it  is  a  Negative 
with  an  undistributed  Predicate.  They  will  not  allow  that 
such  a  Judgment  is  possible ;  but  here  it  appears  as  actual, 
—  nay,  as  the  only  natural  result  of  Premises  to  which, 
according  to  the  Aristotelic  doctrine,  only  a  wholly  unnat- 
ural Conclusion  can  be  given  by  inventing  a  so-called 
Fourth  Figure,  otherwise  not  needed,  and  in  every  respect 
perverted  and  contrary  to  nature.  Of  course,  Sir  William 
Hamilton,  whose  system  expressly  recognizes  these  Nega- 
tive Judgments  (Ani)  with  undistributed  Predicates,  has 
taken  advantage  of  this  fact,  and  pressed  it  as  an  unanswer- 
able argument  against  his  opponents. 

But  to  return  to  the  Aristotelic  doctrine.  The  reason 
ordinarily  given  for  awarding  a  decided  preference  to  the 
First  over  the  other  Figures  is  not  either  of  the  two  here 
alleged,  but  one  which  immediately  results  from  them,  — 
namely,  that  the  Dictum  de  omni  et  nullo,  which  is  h*1^  *■ 

9  M 


194 


MEDIATE  INFERENCE   OR   SYLLOGISM. 


be  a  universal  principle  of  all  reasoning,  is  directly  appli- 
cable only  to  the  First  Figure.  This  Dictum,  which  has 
respect  exclusively  to  the  Quantity  of  Extension,  neces- 
sarily supposes  that  the  order  of  Extension  is  strictly  fol- 
lowed in  the  Syllogism ;  that  is,  that  the  Predicate  in  each 
of  its  three  Judgments  should  be  of  wider  Extension  than 
the  Subject.  This  is  the  case  in  the  First  Figure ;  but  as 
we  have  seen,  it  is  not  so  with  the  others.  In  the  Second, 
the  Subject  of  the  Major,  and  in  the  Third,  the  Subject  of 
the  Minor  Premise,  has  a  wider  Extension  than  the  corre- 
sponding Predicate.  In  order  to  show  that  the  Dictum  is 
universally  applicable,  we  must  be  able  to  reduce  all  Syllo- 
gisms, in  whatever  class  they  may  at  first  be  ranked,  to  the 
First  Figure.  Now,  to  judge  from  the  instance  just  given, 
in  which  we  have  carried  the  same  Syllogism  successively 
through  each  of  the  four  Figures,  such  a  Reduction  can  be 
very  easily  accomplished.  It  is  only  necessary  to  convert 
one  or  both  of  the  Premises.  Recurring  for  a  moment  to 
the  first  mode  of  indicating  the  variations  of  Figure,  — 


I. 

ii. 

in. 

IV. 

MP 

PM 

MP 

PM 

SM 

SM 

MS 

MS 

SP 

.-.SP 

.-.  SP 

/.SP 

it  is  easy  to  see  that  the  Second  Figure  is  reduced  to  the 
First  by  converting  its  Major  Premise ;  the  Third,  by  con- 
verting its  Minor;  and  the  Fourth,  by  converting  both. 
But  as  the  order  of  the  Premises  may  be  transposed,  as  the 
Sumption  and  the  Major  Premise  do  not  always  coincide, 
and  as  the  Judgment  O,  on  the  strict  Aristotelic  doctrine, 
is  not  convertible  at  all,  it  is  not  always  easy  to  tell  which 
Premise  ought  to  be  converted,  and  the  process  of  Re- 
duction practically  becomes  so  complex  and  intricate,  that, 
to  facilitate  it,  an  elaborate  system  and  a  whole  set  of 
mnemonics  have  been  contrived.  These  will  be  explained 
hereafter. 


FIGURE   AND  MOOD.  195 

The  Aristotelic  logicians  appear  to  hesitate,  or  be  in 
doubt,  as  to  the  motives  for  reducing  the  three  lower  Fig- 
ures to  the  First.  At  times,  they  speak  as  if  the  only 
reason  for  such  Reduction  wert  the  one  already  mentioned, 
—  to  reduce  all  Syllogistic  forms  to  system  by  showing  that 
they  are  all  controlled  by  one  governing  principle,  the  Dic- 
tum de  omni  et  nullo.  The  implication  then  is,  that  they 
are  valid  or  competent  forms  of  reasoning,  even  before  such 
Reduction  ;  and  that  they  are  reduced,  therefore,  only  to 
render  them  more  systematic  and  orderly  in  appearance. 
Then,  again,  they  speak  of  proving  them  by  this  Reduction, 
as  if  otherwise  they  were  weak  and  needed  proof,  even  if 
they  were  not  invalid.  The  truth  is,  the  reasoning  under 
either  of  these  Figures  is  just  as  conclusive  as  under  the 
First.  In  neither  case  can  the  Conclusion  be  denied  with- 
out involving  the  denier  in  an  absurdity,  —  that  is,  in  a  con- 
tradiction of  one  of  the  Primary  Axioms  of  Pure  Thought. 
Nay,  more ;  in  certain  cases,  it  is,  in  one  sense,  more 
natural  to  make  inferences  by  the  Second  or  Third  Figure, 
than  by  the  First ;  that  is,  the  particular  object  which  we 
have  in  view  in  the  general  investigation  or  course  of  argu- 
ment which  we  are  pursuing,  may  more  directly  lead  us  to 
the  former  than  to  the  latter.  Thus,  when  we  wish  to 
exclude  something  from  a  class  to  which  it  had  been 
wrongly  assigned,  or  to  disprove  something  which  has  been 
asserted,  we  are  most  frequently  led  to  argue  in  the  Second 
Figure,  since  any  Conclusion  in  this  Figure  must  be  nega- 
tive ;  for  as  the  Middle  Term  is  here  Predicate  in  both 
Premises,  it  cannot  be  distributed  unless  one  of  the  Prem- 
ises is  negative,  and  then,  by  Rule  5,  the  Conclusion  is 
negative.  "  The  arguments,"  says  Whately,  "  used  in  the 
process  called  Abscissio  inftniti,  will,  in  general,  be  the  most 
easily  referred  to  this  Figure.  This  phrase  was  applied  by 
some  logicians  to  a  series  of  arguments  used  in  any  inquiry 
in  which   we  go  on  excluding,  one  by  one,  certain  suppo 


196  MEDIATE  INFERENCE   OR   SYLLOGISM. 

sitions,  or  certain  classes  of  things,  from  that  whose  real 
nature  we  are  seeking  to  ascertain." 

Again,  if  our  design  is  to  establish  exceptions  to  a  pre- 
tended law  or  rule,  —  that  is,  if  we  would  disprove  the  as- 
serted universality  of  the  Proposition,  —  the  Third  Figure 
will  most  commonly  answer  our  purpose,  for  here  all  Con- 
clusions must  be  Particular;  we  prove  that  Some  are,  or 
Some  are  not,  and  thus  disprove  the  assertion  that  All  are 
not,  or  All  are.  Conclusions  in  the  Third  Figure  must  be 
Particular,  because  both  Terms  of  the  Conclusion  appear 
as  Predicates  in  the  two  Premises ;  hence,  if  these  Prem- 
ises are  both  Affirmatives,  their  Predicates  are  Particular ; 
and  if  one  of  them  is  Negative,  the  Conclusion  can  only  be 
a  Particular  Negative,  since  a  Universal  Negative  distrib- 
utes both  its  Terms. 

Because  the  two  lower  Figures  are  thus  not  only  valid 
in  themselves,  but  peculiarly  appropriate  for  certain  pur- 
poses, some  logicians  hold  that  it  is  unnecessary  to  reduce 
them  to  the  First  Figure.  Each  of  the  three,  they  main- 
tain, has  its  own  functions  and  its  own  governing  principle. 
The  principle  which  is  assigned  to  the  First,  needs  but  to 
be  slightly  modified  in  order  to  be  directly  applicable  to 
the  Second  or  the  Third ;  since  all  three  are  but  various 
applications  of  the  same  Axioms  of  Thought.  Thus,  if  the 
Dictum  de  omni  et  nullo  be  considered  as  the  principle  for 
the  First  Figure,  for  the  Second  we  have  the  Dictum  de 
diverso,  —  that  if  one  Term  is  contained  in,  and  another  ex- 
cluded from,  a  third  Term,  then  they  are  excluded  from  each 
other.  For  the  Third  Figure,  the  principle  is  called  the 
Dictum  de  exemplo,  —  that  two  Terms  which  contain  a  com- 
mon part  partly  agree  ;  or,  if  one  contains  a  part  which  the 
other  does  not,  they  partly  differ. 

Reduction  is  not  essential,  therefore,  but  it  is  certainly 
convenient ;  the  reasoning  does  not  become  more  cogent  by 
being  reduced  to  the  First  Figure,  but  it  is  rendered  more 


FIGURE  AND  MOOD.  197 

perspicuous,  more  simple  and  natural  in  expression,  and 
any  fallacies  in  it,  which  might  otherwise  escape  notice, 
become  at  once  so  obvious  that  they  cannot  avoid  detection. 
The  whole  theory  of  argumentation,  moreover,  is  rendered 
more  systematic  and  elegant,  when  its  numerous  modes 
are  reduced  to  a  very  few  fundamental  forms,  the  validity 
of  which  is  so  manifest  that  they  do  not  need  to  be  tested 
by  the  application  of  previously  determined  rules. 

The  proper  relative  position  of  the  three  Judgments  of 
a  Syllogism  appears  so  obvious,  on  the  Aristotelic  doctrine, 
that  it  has  usually  been  taken  for  granted.  If  we  reason 
only  in  order  to  instruct,  to  convince,  or  to  refute,  —  and 
no  other  purpose  seems  to  have  been  contemplated  by  the 
old  logicians,  —  the  natural  order  of  Thought  seems  to  be, 
that  the  Ground  or  Reason  should  precede  the  Conse- 
quence ;  that  is,  that  the  Premises,  as  their  name  imports, 
should  precede,  and,  as  it  were,  effectuate  the  Conclusion. 
And  as  regards  the  two  Premises,  if  the  reasoning  is  ex- 
clusively in  the  Quantity  of  Extension,  the  Major  should 
be  placed  before  the  Minor,  the  Sumption  or  General  Rule 
before  the  Subsumption. 

The  Mood  of  a  Syllogism  is  the  value  of  its  three  Judg- 
ments considered  in  respect  to  their  Quantity  and  Quality. 
Since  there  are  but  four  kinds  of  Judgments  as  thus  viewed, 
indicated  respectively  by  the  four  vowels  A,  E,  I,  and  O, 
it  is  evident  that  three  of  these  letters  must  express  any 
possible  Mood.  When  we  have  ascertained  its  Mood  and 
Figure,  the  classified  place  and  formal  value  of  a  Syllogism 
are  determined.  For  instance,  E  I  O,  Fig.  I.,  and  A  A  I, 
Fig.  III.,  are  thus  expressed  :  — 


Fig.  I. 

Fig.  in. 

No  M  is  P  ; 

E 

All  M  are  P ; 

A 

Some  S  are  M ; 

I 

All  M  are  S ; 

A 

Some  S  are  not  P. 

O 

.•.  Some  S  are  P. 

I 

198  MEDIATE  INFERENCE   OR   SYLLOGISM. 

As  only  four  Judgments  are  possible,  and  three  are 
necessary  to  constitute  a  Syllogism,  the  whole  number  of 
Moods  can  be  numerically  determined.  Only  sixty-four 
different  arrangements  can  be  made  out  of  four  letters 
taken  three  at  a  time ;  hence,  sixty-four  Moods  are  con- 
ceivable. But  the  greater  number  of  these  are  invalid,  as 
contradicting  one  or  more  of  the  General  Rules  which 
govern,  as  we  have  seen,  all  forms  of  Mediate  Inference. 
The  elimination  of  these  invalid  forms  can  be  more  easily 
effected,  if  we  first  reduce  the  expression  of  a  Mood  to  its 
simplest  form. 

Strictly  speaking,  only  the  two  letters  which  denote  the 
Premises  need  to  be  taken  into  account ;  for  the  Quantity 
and  Quality  (and  therefore  the  letter)  of  the  Conclusion 
are  determined  by  those  of  the  Premises.  Each  Mood, 
then,  being  designated  by  only  two  letters,  and  only  six- 
teen different  arrangements  being  possible  of  four  letter? 
taken  two  at  a  time,  all  conceivable  Moods  are  contained 


in  the  following 

list :  — 

1.)  A  A 

2.)  E  A 

3.)  I  A 

4.)    OA 

AE 

E  E 

ie  y 

OE 

AI 

EI 

ii  • 

OI 

AO 

EO 

IO   v 

oo 

The  Rule  that  from  two  Negative  Premises  no  Conclusion 
can  be  drawn,  excludes  four  from  this  list,  namely,  E  E, 
E  O,  O  E,  and  O  O.  The  Rule  that  no  Conclusion  can  be 
drawn  from  two  Particular  Premises,  excludes  three  more, 
namely,  I  I,  I  O,  and  O  I.  Finally,  I  E  is  excluded  be- 
cause its  Negative  Conclusion  distributes  the  Major  Term, 
which  is  undistributed  in  I,  the  Major  Premise;  but 
according  to  Rule  6,  neither  Term  can  be  distributed  in  the 
Conclusion,  if  it  was  not  distributed  in  the  Premise.  We 
may  here  observe,  that  the  violation  of  this  last  Rule,  in 
respect  to  the  Major  Term,  is  called  illicit  process  of  the 


FIGURE  AND  MOOD.  199 

Major ;  in  respect  to  the  Minor  Term,  it  is  called  illicit 
process  of  the  Minor. 

These  exclusions  being  effected,  there  remain  but  eight 
valid  Moods,  namely,  A  A,  A  E,  A  I,  A  O,  E  A,  E  I, 
I  A,  and  O  A.  Not  all,  even  of  these  eight,  however, 
afford  a  valid  Syllogism  in  each  of  the  four  Figures;  for 
the  altered  position  of  the  Middle  Term  may  cause  the 
greater  number  of  them  to  offend  against  the  Rules  which 
forbid  both  an  undistributed  Middle  and  an  Illicit  Process 
whether  of  the  Major  or  Minor  Term.  Special  Rules 
have  been  enounced  for  each  of  the  Figures,  which  will 
enable  us  to  make  the  further  exclusions  that  are  requisite. 
It  should  be  observed,  that  these  Special  Rules  contain  no 
new  principle,  but  are  immediately  deducible  from  the 
General  Rules,  that  have  already  been  established  for  all 
Syllogisms  ;  taking  these  General  Rules  in  connection,  how- 
ever, with  the  two  axioms  by  which  the  Aristotelians  de- 
termine the  implicit  Quantity  of  the  Predicate ;  namely, 
that,  in  all  Affirmative  Judgments,  the  Predicate  is  Par- 
ticular, and  that,  in  all  Negative  Judgments,  the  Predicate 
is  Universal.  This  deduction  may  be  left  as  an  exercise 
for  the  learner.  We  will  here  consider  the  Special  Rules 
under  that  theory  which  regards  every  Mediate  Inference 
as  proceeding  from  the  Subsumption  of  a  particular  case 
under  a  General  Rule  or  Sumption  ;  little  more  than  an 
alteration  of  phraseology  will  be  needed  to  adapt  them  to 
the  theory  in  which  we  speak  only  of  Major  and  Minor 
Premises. 

The  Special  Rules  for  the  First  Figure  are,  — 

1.  The  Sumption  must  be  Universal ; 

2.  The  Subsumption  must  be  Affirmative. 

These  two  Rules  exclude  I  A,  O  A,  A  E,  and  A  O. 
There  remain  A  A,  E  A,  A  I,  and  E  I,  as  the  only  valid 
Moods  in  this  Figure ;  and  these  are  named  Barbara,  Ce- 
larent,  Darii,  and  Ferio.     Observe  that  the  three  vowels 


200  MEDIATE   INFERENCE   OR   SYLLOGISM. 

in  each  of  these  names  denote  the  Mood  of  the  Syllogism 
to  which  it  is  applied ;  and  the  same  is  true  of  the  technical 
names  which  "will  be  given  to  the  valid  Moods  in  the  other 
Figures. 

The  Special  Rules  for  the  Second  Figure  are,  — 

1.  The  Sumption  must  be  Universal ; 

2.  One  of  the  Premises  must  be  Negative,  and  there- 

fore the  Conclusion  must  be  Negative. 

These  Rules  exclude  I  A,  O  A,  A  A,  and  A  I ;  the? 
there  remain  as  valid  in  the  Second  Figure  only  the  four 
Moods  which  have  been  named  Cesare,  Camestres,  Festino 
and  Baroko. 

The  Special  Rules  for  the  Third  Figure  are,  — 

1.  The  Subsumption  must  be  Affirmative  ; 

2.  The  Conclusion  must  be  Particular. 

Throwing  out  A  E  and  A  O  under  these  Rules,  there 
remain  for  the  Third  Figure  six  Moods,  named  BaraptL 
Biennis,  Batisi,  Felapton,  Bokardo,  and  Ferison. 

The  Special  Rules  for  the  Fourth  Figure  are,  — 

1.  If  the  Sumption  is  Affirmative,  the  Subsumption 
must  be  Universal. 

2.  If  either  Premise  is  Negative,  the  Sumption  must  be 
Universal. 

3.  If  the  Subsumption  is  Affirmative,  the  Conclusion 
must  be  Particular. 

Rejecting  A  I,  A  O,  and  O  A,  as  offending  against 
these  Rules,  there  remain  only  five  Moods,  called  Bra- 
mantip,  Camenes,  Bimaris,  Fesapo,  and  Fresison,  as  valid 
in  the  Fourth  Figure. 

Taking  the  four  Figures  together,  therefore,  there  are 
nineteen  valid  Moods  ;  but  as  fifteen  of  these  can  be  re- 
duced to  those  of  the  First  Figure,  there  are  only  four 
Moods  which  are  at  once  valid,  natural,  and  perspicuous. 
Regarding  the  last  vowel  in  the  names  of  these  four  (Bar- 
bara^    Celarent,  Barii,  Ferio'),  we  see  that  these  are  just 


FIGURE   AND   MOOD.  201 

sufficient  to  prove  the  four  fundamental  Judgments,  A,  E, 
I,  and  O. 

If  we  exclude  the  Fourth  Figure  altogether,  considering 
Bramantip,  Camenes,  &c.  as  indirect  Moods  of  the  First, 
there  are  but  fourteen  direct  Moons.  On  the  other  hand, 
since  from  every  Syllogism  with  a  Universal  Conclusion 
we  can  obtain,  by  Subalternation,  a  Particular  Conclusion 
also,  there  are  five  other  indirect  Moods,  which  are  anony- 
mous, making  twenty-four  in  all.  Tims,  A  A  in  the  First 
yields  I,  as  well  as  A,  for  a  Conclusion ;  and  from  E  A  in 
the  Second,  we  may  conclude  not  only  E,  but  O.  But 
these  anonymous  Moods,  besides  being  indirect,  are  prac- 
tically useless  ;  since  it  is  idle  to  infer  some  only,  when  the 
Premises  warrant  the  inference  of  all. 

Rejecting  the  Fourth  Figure  and  the  indirect  Moods, 
it  will  be  seen,  from  examining  the  last  vowel  in  each  of 
the  names,  that  A  is  proved  only  in  one  Figure  and  on* 
Mood  ;  E  in  two  Figures  and  three  Moods  :  I  in  two  Fig- 
ures and  four  Moods ;  and  O  in  three  Figures  and  six 
Moods.  "For  this  reason,"  says  Mr.  Mansel,  "A  is  de- 
clared by  Aristotle  to  be  the  most  difficult  proposition  to 
establish,  and  the  easiest  to  overthrow ;  O,  the  reverse. 
And,  generally,  Universals  are  most  easily  overthrown, 
Particulars  more  easily  established." 

The  names  of  all  the  valid  Moods  have  been  put  to- 
gether into  the  following  mnemonic  hexameters,  which 
deserve  careful  study,  not  only  as  a  complete  artificial 
system  for  the  Reduction  of  all  the  Moods  of  the  subordi- 
nate Figures  to  those  of  the  First,  (for  which  purpose  the 
names  were  invented,)  but  as  a  literary  curiosity.  They 
have  been  in  use  in  the  Schools,  as  an  aid  to  the  mem- 
ory, for  over  six  centuries,  their  authorship  being  un- 
known. Mr.  DeMorgan  calls  them  "the  magic  words 
which  are  more  full  of  meaning  than  any  that  ever  were 
made.*'     Sir  William  Hamilton  says  of  them  that  "  there 

9* 


202  MEDIATE  INFERENCE   OR   SYLLOGISM 

we  few  human  inventions  which  display  a  higher  inge- 
nuity." 

Barbara,  Celarent,  Darii,  Ferioque  prioris. 
Cesare,  Camestres,  Festino,  Baroko  secundae. 
Tertia  Darapti,  Dif  amis,  Datisi,  Felapton, 
Bokardo,  Ferison  habet.     Quarta  insupcr  addit 
Bramantip,  Camenes,  Dimaris,  Fesapo,  Fresison. 

If,  rejecting  the  Fourth  Figure,  we  consider  its  contents 
as  indirect  Moods  of  the  First,  instead  of  the  first  line,  the 
two  following  should  be  substituted  :  — 

Barbara,  Celarent,  Darii,  Ferio,  Baralip-<ow, 

CeLANTES,  DABITIS,  FAPESMO,   FRISESOM-OTMTn, 

the  final  syllables  in  italics  being  only  euphonic. 

As  already  mentioned,  the  three  vowels  in  each  of  these 
names  indicate  the  Quantity  ar.d  Quality  of  the  three  Judg- 
ments which  form  the  Syllogism.  The  consonants  in  the 
names  belonging  to  the  First  Figure  have  no  special  mean- 
ing ;  but  of  those  in  the  other  Figures,  every  consonant 
(except  t  and  n,  which  are  merely  euphonic)  indicates 
some  step  to  be  taken  in  the  process  of  reducing  the  Mood 
to  a  Mood  of  the  First  Figure. 

The  initial  consonant,  which  is  either  B,  C,  D,  or  F, 
indicates  that  Mood  of  the  First  Figure  (.Barbara,  Cela- 
rent, Darii,  or  .Ferio)  to  which  the  Reduction  brings  us. 
Thus,  Cesare  and  Camestres  are  reduced  to  Celarent;  Fes- 
tino, Felapton,  &c,  to  Ferio.  The  other  consonants  show 
how  the  Reduction  is  made,  m  indicates  that  the  Premises 
are  to  be  transposed  ;  s  and  p,  that  the  Judgment  indicated 
by  the  vowel  immediately  preceding  is  to  be  converted,  — 
s,  that  it  is  to  be  converted  simply,  while  p  signifies  the 
conversion  per  accidens. 

k,  which  occurs  in  the  names  of  only  two  Moods,  Ba- 
roko and  Bokardo,  denotes  that  the  Judgment  indicated 
by  the  preceding  vowel  is  to  be  left  out,  another  sub- 
stituted foi  it,  and  the  process  to  be  then  completed  by 


FIGURE  AND  MOOD. 


203 


*  Reduction  per  impossibile,  which  will  be  explained  here- 
after. 

A  few  examples  will  sufficiently  illustrate  the  process. 
The  name  Disamis  indicates  the  following  Syllogism  of 
the  Third  Figure,  which  is  to  be  reduced  to  Darii  of  the 
First,  by  converting  simply  its  Major  Premise,  transposing 
its  Premises,  and  then  converting  its  Conclusion. 

Disamis  reduced  to  Dabii. 


Some  M  are  P ; 
All  M  are  S  ; 
.•.  Some  S  are  P. 

Some  wars  are  justifiable  ; 
All  wars  are  inexpedient ; 
.*.  Some  inexpedient  acts  are 
justifiable. 


All  M  are  S  ; 
Some  P  are  M ; 
.*.  Some  P  are  S. 

All  wars  are  inexpedient ; 
Some  justifiable  acts  are  wars ; 
.*.  Some  justifiable  acts  are  inex- 
pedient. 

Festino  of  the  Second  is  reduced  to  Ferio  of  the  First 
Figure,  by  converting  simply  its  Major  Premise. 

Festino  reduced  to  Ferio. 


No  P  is  M  ; 
Some  S  are  M  ; 
.*.  Some  S  are  not  P. 

No  ruminant  is  solid-hoofed; 


Some   herbivora    are    solid- 
hoofed  ; 

Some  herbivora  are  not  rumi- 
nant. 


No  M  is  P  ; 
Some  S  are  M  ; 
,\  Some  S  are  not  P. 

No  solid-hoofed  animal  is 

ruminant ; 
Some  herbivora  are  solid- 
hoofed  ; 
.  Some   herbivora   are    not 
ruminant. 


Fesapo  of  the  Fourth  is  reduced  to  Ferio  of  the  First 
Figure,  by  converting  both  its  Premises,  the  Major  simply, 
md  the  Minor  per  accidens. 

Fesapo  reduced  to  Ferio. 

No  P  is  M  ;  No  M  is  P  ; 

All  M  are  S ;  Some  S  are  M ; 

/.  Some  S  are  not  P.  .\  Some  S  are  not  P. 


204  MEDIATE  INFERENCE   OR   SYLLOGISM. 

No  Hindoo  is  white ;  No  white  is  a  Hindoo ; 

All  whites  are  civilized  ;  Some  civilized  are  whites  ; 

.*.  Some  civilized  are  not  Hindoos.      .\  Some    civilized    are    not 

Hindoos. 

Baroko  and  Bokardo  have  been  stumbling-blocks  to  the 
logicians.  In  order  to  reduce  either  of  them  to  the  First 
Figure,  the  Premise  which  needs  to  be  converted  is  O  ; 
but  according  to  the  old  doctrine,  O  is  inconvertible.  To 
overcome  this  difficulty,  the  logicians  invented  the  awk- 
ward, roundabout,  and  operose  process  which  they  called 
Reduction  per  Impossibile.  Through  a  Syllogism  in  Bar- 
bara, they  proved,  not  directly  that  the  Conclusion  in 
Baroko  and  Bokardo  is  true,  but  that  its  Contradictory  is 
false ;  now,  according  to  the  Axiom  of  Excluded  Middle 
(that  two  Contradictories  cannot  both  be  false),  this  is  an 
indirect  method  of  proving  that  the  Conclusion  is  true. 
The  process  is  as  follows. 

Of  course,  both  Premises  in  every  Syllogism  are  pre- 
sumed to  be  true  ;  then,  any  Conclusion  which  contradicts 
either  one  of  them  must  be  false.  Now,  k  indicates,  that, 
instead  of  the  Premise  signified  by  the  vowel  (O)  imme- 
diately preceding,  we  are  to  substitute  the  Contradictory 
of  the  Conclusion ;  and  as  this  Conclusion  is  O,  its  Contra- 
dictory is  A.  But  from  the  two  Premises  (A  A)  thus 
obtained,  we  have  a  Conclusion  which  contradicts  the  origi- 
nal Premise,  O.  Then  the  substituted  Judgment  in  A 
(which  is  the  Contradictory  of  the  original  Conclusion) 
must  be  false  ;  and  therefore  the  original  Conclusion  itself 
is  true.  This  is  not  exactly  reducing  the  Syllogism  to  the 
First  Figure,  but  it  is  indirectly  proving,  through  the  First 
Figure,  that  the  Conclusion  of  the  Syllogism  must  be  true, 
because  its  Contradictory  is  false. 

Baroko  reduced  to  Barbara. 

All  P  are  M ;  All  P  are  M  ;  [elusion.) 

Some  S  are  not  M  ;        All  S  are  P  ;  (Contradictory  of  former  Con- 

.  Some  S  are  not  P.      .%  All  S  are  M.    (Contradicts   former    Elinor 

Premise.) 


FIGURE   AND  MOOD. 


205 


All  M  are  S  ; 
Some  S  are  not  P. 

As   this    Conclusion 


Bokardo  reduced  to  Barbara. 

Some  M  are  not  P  ;         All  S  are  P  ;  (Contradictory    of    former 
All  M  are  S  ;       Conclusion). 

All  M  are  P.    (Contradicts  former  Major 
Premise.) 

in  Barbara  cannot  be  time,  its 
Premise,  which  is  the  Contradictory  of  the  former  Con- 
clusion, must  be  false ;  then  the  original  Conclusion  itself 
is  true. 

All  this  is  awkward  enough.  Whately  and  others 
rightly  remark,  that  these  two  difficult  Syllogisms  can  be 
reduced  in  a  much  simpler  and  more  elegant  manner, 
through  converting  one  of  their  Premises  by  Contrapo- 
sition. Thus,  let  Baroko  be  now  called  Fakoro,  and  let 
Bokardo  be  named  Dokamok  (the  substitution  of  these  two 
names  will  not  spoil  the  mnemonic  hexameters)  ;  and  let 
K  indicate  Conversion  by  Contraposition. 

Fakoro  reduced  to  Ferio. 


All  P  are  M  ; 
Some  S  are  not  M ; 
.*.  Some  S  are  not  P. 
All  murders  are  intentional ; 

Some  homicides  are  not  inten- 
tional ; 
.  Some   homicides  are  not  mur- 
ders. 

Dokamok  reduced  to 

Some  M  are  not  P  ; 
All  M  are  S  ; 
,\  Some  S  are  not  P. 

by  Contraposition,)     . 
Some  imprudent  acts   are 

not  vicious  ; 
All  imprudent  acts  are  foolish ; 


No  not-M  is  P  ; 
Some  S  are  not-M  ; 
,\  Some  S  are  not  P. 

No  unintentional  act  is  a 

murder ; 
Some  homicides  are  unin- 
tentional ; 
.*.  Some   homicides  are    not 
murders. 

Darii. 
All  M  are  S  ; 
Some  not-P  are  M ; 
*.  Some  not-P  are  S  ;  (or.  convert 
\  Some  S  are  not  P. 
All  imprudent  acts  are  foolish ; 


Some    not-vicious 
imprudent ; 


acts    are 


206  MEDIATE  INFERENCE   OR  SYLLOGISM. 

•.  Some  foolish   acts  are  not    .*.  Some     not-vicious     acts    are 
vicious.  foolish ; 

.*.  Some    foolish    acts    are    not 
vicious. 

These  examples  show  that,  after  Dokamok  has  been  re- 
duced to  Darii,  the  Conclusion  must  be  contraponed  back 
again,  if  we  would  have  it  in  its  original  form. 

Ingenious  as  this  whole  system  of  Reduction  is,  it  is 
needlessly  artificial  and  complex.  The  sole  reason  for  re- 
ducing Syllogisms  to  the  First  Figure,  we  have  said,  is 
to  exhibit  the  reasoning  in  its  simplest  and  most  natural 
form,  and  in  that  in  which  its  validity,  or  invalidity,  is  most 
readily  perceived.  A  few  simple  Rules  may  be  given 
which  will  enable  the  learner  to  accomplish  this  object  at 
once,  in  whatever  Figure  the  argumentation  may  originally 
be  propounded,  and  even  without  knowing  what  this  Fig- 
ure is. 

1.  Every  process  of  reasoning  must  consist  of  a  Judg- 
ment which  is  to  be  proved,  and  of  one  or  two  other  Judg- 
ments alleged  in  its  support ;  the  former  is  the  Conclusion, 
the  latter  are  the  Premises.  The  first  step  is  to  reduce 
each  of  these  Judgments  to  its  simplest  logical  form,  — 
that  is,  to  a  Subject  and  Predicate  connected  by  the  pres- 
ent tense  (affirmative  or  negative)  of  the  verb  to  be.  Care 
must  be  taken  to  determine  accurately  the  Quantity  and 
Quality  of  each  of  the  Judgments. 

2.  The  Middle  Term  is  that  which  does  not  appear  in 
the  Conclusion.  If  no  such  Term  is  found  in  the  Prem- 
ises, the  Inference  is  Immediate,  and  must  be  tried  by  the 
principles  laid  down  in  the  preceding  chapter,  concerning 
Conversion,  Opposition,  &c.  If  there  is  a  Middle  Term, 
the  Inference  is  Mediate  ;  then  the  Maj\  r  Premise  is  that 
Judgment  in  which  this  Middle  Term  appears  connected 
with  the  Predicate  of  the  Conclusion ;  the  Minor  Premise, 
that  in  which  it  is  connected  with    the    Subject   of  the 


CONDITIONAL   SYLLOGISMS.  207 

Conclusion.  If  only  one  Premise  is  given  in  the  original 
statement,  the  other  may  be  easily  supplied  by  a  moment's 
consideration,  as  its  two  naked  Terms  are  known,  and  its 
Quantity  and  Quality  may  be  inferred,  through  the  General 
Rules  already  given  for  all  Syllogisms,  from  the  Quantity 
and  Quality  of  the  Conclusion  and  the  given  Premise. 

3.  The  First  Figure  requires  the  Middle  Term  to  be  the 
Subject  of  the  Major,  and  the  Predicate  of  the  Minor, 
Premise.  If,  in  the  Premises  as  determined,  the  Terms  do 
not  already  appear  in  this  order,  one  or  both  must  be  con- 
verted, either  simply,  or  per  accidens,  or  by  Contraposition. 

There  can  be  no  difficulty  in  the  application  of  these 
Rules,  which  does  not  arise  from  some  ambiguity  in  the  lan- 
guage of  the  original  statement ;  and  to  resolve  such  am- 
biguity is  the  business,  not  of  the  logician,  but  of  the  gram- 
marian and  the  lexicographer.  But  a  few  cases  will  be 
incidentally  resolved  when  we  come  to  treat  of  Fallacies,  a 
subject  which  cannot  be  fully  considered  without  some- 
times stepping  out  of  the  province  of  Pure  Thought. 

2.    Conditional  Syllogisms. 

Thus  far  we  have  treated  exclusively  of  the  purely  Cate 
gorical  Syllogism,  in  which  each  of  the  component  Judg- 
ments can  be  reduced  to  one  or  the  other  of  the  two  Cate- 
gorical formulas,  A  is  B,  or  A  is  not  B.  The  reasoning  in 
thii  case,  as  we  have  seen,  depends  upon  the  two  Axioms 
of  Identity  and  Non-Contradiction.  We  come  now  to 
another  class  of  Syllogisms,  dependent  upon  the  Axioms 
of  Reason  and  Consequent,  and  Excluded  Middle. 

A  Conditional  Syllogism  is  one  of  which  the  Major  Prem- 
ise, and  only  the  Major  Premise,  is  a  Conditional  Judgment. 
There  are  three  kinds  of  such  Syllogisms,  corresponding  to 
the  three  classes  into  which  Conditional  Judgments  are 
divided  ;  namely,  the  Hypothetical,  the  Disjunctive,  and  the 


208  MEDIATE   INFERENCE   OR   SYLLOGISM. 

Dilemmatic  or  Hypothetico-Disjunctive.     The  following  are 
examples  of  each. 

Hypothetical.  Disjunctive. 

If  A  is  B,  C  is  D  ;  A  is  either  B  or  C ; 

A  is  B  ;  A  is  B  ; 

.\  C  is  D.  .\  A  is  not  C. 

Dilemmatic  or  Hypothetico-Disjunctive. 

If  A  is  B,  C  is  either  D  or  Bs 
C  is  neither  D  nor  E ; 
.*.  A  is  not  B. 

These  Terms  may  be  quantified  in  the  Minor  Premise, 
as  in  Categorical  Syllogisms,  and  the  Conclusion  will  still 
he  valid,  if  its  proper  Quantity  be  assigned  to  it  according 
to  the  Rules  already  given.  Thus,  if  the  Minor  Premise 
of  the  preceding  Hypothetical  be  "  All  A  are  B,"  we  may 
conclude  that  "All  C  are  D";  but  if  we  know  only  that 
"  Some  A  are  B,"  we  can  only  conclude  that  "  Some  C 
are  D."  We  may  likewise  use  the  quantification  of  Sin- 
gulars, and  say,  "  this  A,"  or  "  in  certain  cases,  A  is  B  "  ; 
then,  "  i*  this  case,"  or  "  in  the  same  cases,"  C  is  D. 

Dr.  Thomson  seems  to  be  wrong,  therefore,  when  he 
gives  the  following  as  an  instance  of  a  Hypothetical  Syllo- 
gism, Figure  I.  in  which  each  of  the  three  Judgments  is 
Hypothetical. 

In  cases  where  M  is  N,  C  is  D. 

In  cases  where  A  is  B,  M  is  N. 

In  cases  where  A  is  B,  C  is  D. 
Here,  the  supposed  Condition,  "  in  cases  where  A  is  B,' 
is  only  an  awkward  quantification  of  the  Minor  Premise 
and  the  Conclusion,  equivalent  to  "  in  certain  cases"  or 
"  some  M  is  N  "  ;  therefore,  in  these  cases,  or  some,  C  is  D. 
The  reasoning  does  not  turn  upon  this  phrase,  "  in  cases 
where  A  is  B,"  as  a  condition,  the  Consequent  being 
evolved   from   it ;    it  turns  upon   it  only  as  a  limitation, 


CONDITIONAL   SYLLOGISMS.  209 

showing  in  how  many  cases  the  reasoning  is  applicable. 
The  reasoning  does  rest  exclusively  upon  the  Major 
Premise,  where  the  corresponding  phrase,  "  in  cases  where 
M  is  N,"  is  a  true  condition,  the  Consequent  being  evolved 
from  it,  and  the  whole  argumentation  being  governed  by 
the  Axiom  of  Reason  and  Consequent. 

This  error  has  led  Dr.  Thomson  into  a  more  serious  one. 
Not  perceiving  that  Hypothetical  Reasoning  is  distinct  in 
kind  from  Categorical,  being  governed  by  a  different  Axiom 
of  Thought,  he  has  overlooked  the  principle  that,  from 
affirming  the  Consequent  of  a  Reason,  no  Conclusion  can  be 
drawn,  and  has  presented  the  following  as  a  valid  Syllo- 
gism :  — 

In  cases  where  C  is  D,  M  is  N ; 
In  cases  where  A  is  B,  M  is  N ; 
.*.  In  cases  where  A  is  B,  C  is  D. 
But  here  the  Minor  Premise  only  affirms  that  "  M  is  N," 
which  is  the  Consequent  of  the  hypothesis  in  the  Major 
Premise  ;    and  therefore  the  Conclusion  is  illogical ;   the 
Middle  Term  is  not  distributed.     This  can  be  easily  seen 
from  the  following  example,  the   Conclusion  of  which  is 
evidently  a  non  sequitur. 

If  you  whip  him,  the  boy  cries ; 
If  you  take  away  his  toys,  the  boy  cries ; 
.•.If  you  take  away  his  toys,  you  whip  him. 

Then,  in  a  Conditional  Syllogism,  it  is  only  the  Major 
Premise  which  is  a  Conditional  Judgment ;  for  the  reason- 
ing turns  upon  the  relation  of  Reason  and  Consequent,  and 
this  relation,  being  once  affirmed  in  the  Major  Premise, 
affords  all  the  material  requisite  for  the  Inference.  Both 
the  Minor  Premise  and  the  Conclusion  must  be  Categorical ; 
the  Major  contains  all  the  Terms  which  appear  in  either  of 
them  ;  whereas,  the  Minor  Premise  of  a  Categorical  Syllo- 
gism contains  a  new  Term,  which  did  not  appear  in  the 
Major.     If,  then,  both  Premises,  or  one  Premise  and  Con- 


210  MEDIATE   INFERENCE   OR   SYLLOGISM. 

elusion,  are  Conditional  Judgments,  the  reasoning  is,  in 
fact,  Categorical,  and  depends  upon  the  Axioms  of  Identity 
and  Non-Contradiction.  This  is  easily  seen  in  the  case  of 
a  Disjunctive  Syllogism,  whose  form  is  determined  by  the 
Axiom  of  Excluded  Middle. 

Every  A  is  either  X  or  Y  ; 

But  B  is  A  ; 

Then  B  is  either  X  or  Y. 
Here   the  reasoning  is  evidently  Categorical ;    the  Minor 
Premise  introduces  a  new  Term,  B,  not  contained  in  the 
Major  Premise,  and  therefore  the  Conclusion  is  also  Dis- 
junctive. 

Endeavoring  to  prove  that,  in  a  Disjunctive  Syllogism, 
not  only  the  Major,  but  the  Minor  Premise  or  the  Conclu- 
sion, may  be  a  Disjunctive  Judgment,  Dr.  Thomson  pre- 
sents the  following  as  a  valid  example  :  — 
C,  D,  and  E  are  B  ; 
C,  D,  and  E  =  A ; 
.-.  A  is  B. 
This  is  not  a  Disjunctive  Syllogism  at  all,  as  neither  of  the 
three  Judgments  is  Disjunctive  ;  the  three  Concepts  which 
constitute  the  Middle  Term  are  not  taken  disjunctively, 
but  collectively  ;  that  is,  one  of  them  does  not  exclude  the 
others,  but  requires  the  presence  of  the  others,  in  order  to 
constitute  the  Predicate.    They  form  one  compound  Term. 
Thus,  let  (7,  D,  and  E  =  M,  and  make  the  substitution. 
Then   the  Syllogism  assumes  this  form,  and  is  evidently 

Categorical. 

M  is  B ; 
M  =  A; 
.-.  A  is  B. 

The  Axiom  of  Reason  and  Consequent  is  explicated,  as 
we  have  seen,  into  these  two  principles  ;  —  to  affirm  the 
Reason  or  the  Condition  is  also  to  affirm  the  Consequent  or 
the  Conditioned;  and  to  deny  the  Consequent  is  also  to  deny 


CONDITIONAL   SYLLOGISMS.  211 

the  Reason.  The  application  of  these  principles  gives  us, 
from  the  same  Major  Premise,  two,  and  only  two,  valid 
Moods  of  the  Hypothetical  Syllogism,  —  namely,  the 
Modus  Ponens  and  the  Modus  Tollens.     Thus :  — 


If  A  is  B,  C  is  D. 


Modus  Ponens. 


Modus  Tollens. 


C  is  not  D  ; 
Then  A  is  not  B, 


AisB; 
Then  C  is  D. 
The  following  are  examples  of  these  formulas  :  — 
Modus  Ponens. 
If  matter  is  essentially  inert,  every  change  in  it  must  be 

produced  by  mind ; 
But  matter  is  essentially  inert ; 
Then  all  changes  in  it  are  produced  by  mind. 

Modus  Tollens. 
If  the  moon  shines  by  its  own  light,  it  must  always  be  full ; 
But  it  is  not  always  full ; 
Then  it  does  not  shine  by  its  own  light. 

We  have  said  that  there  are  only  two  valid  Moods,  be- 
cause, from  denying  the  Reason,  or  from  affirming  the  Con- 
sequent, nothing  follows.  The  Consequent  may  follow  from 
some  other  Reason  than  the  particular  one  assigned  in  the 
Major  Premise  ;  and  the  original  Axiom  only  affirms  the 
necessity  of  some  Reason  or  other,  not  of  any  particular 
one.  It  is  true,  that  the  Minor  Premise  may  be  quantified 
with  the  predesignations  all,  some,  or  this,  and  correspond- 
ing Conclusions  will  follow.  The  different  forms  which 
thus  result  may,  if  we  please,  be  called  Moods  also. 

The  Major  Premise,  or  Sumption,  in  either  of  the  pre- 
ceding examples,  may  be  converted  by  Contraposition ; 
and  the  result  will  be,  that  what  was  the  Modus  Tollens 
becomes  the  Modus  Ponens,  and  vice  versa.  These  two 
Moods  are  thus  shown  to  be  really  one  ;  and  this  is  pre- 
cisely what  we  should  expect,  for  the  two   principles  by 


212  MEDIATE  INFERENCE   OR   SYLLOGISM. 

which  they  are  governed  are  only  two  explications  of  one 
Axiom  of  Thought.  Thus,  the  last  preceding  example, 
which  is  now  the  Modus  Tollens,  becomes  the  following,  if 
we  contrapone  the  Sumption :  — 

If  the  moon  is  not  always  full,  it  does  not  shine  by  its  own 

light; 
But  it  is  not  always  full ; 
Then  it  does  not  shine  by  its  own  light. 

Here  the  Subsumption  posits  what  is  now  the  Reason, 
(though  both  are  negative  in  form,)  and  therefore  the 
Conclusion  posits  the  Consequent.  Hence  the  reasoning 
has  now  become  the  Modus  Ponens. 

Summing  up  what  has  been  said,  it  appears  that  the 
Hypothetical  Syllogism  is  subject  to  these  three  Special 
Rules :  — 

1.  It  consists  of  three  Judgments,  and  only  three ;  but  in 
these  Judgments  there  may  be  more  than  three  Terms. 

2.  In  respect  to  Quantity  and  Quality,  the  Sumption 
must  always  be  Affirmative  and  Universal,  while  the  Sub- 
sumption  may  vary  in  either  of  these  relations. 

3.  The  Conclusion  is  regulated,  both  in  Quantity  and 
Quality,  by  that  member  of  the  Sumption  which  is  not 
subsumed,  agreeing  with  it  in  both  these  respects  in  the 
Modus  Ponens,  and  differing  from  it  in  both  in  the  Modus 
Tollens. 

The  Sumption  in  the  last  example  (after  Contraposition) 
may  seem  not  to  conform  to  the  second  of  these  Rules  ;  for 
it  appears  to  be  Negative  in  Quality.  But  if  closely  ex- 
amined, the  negative  particle  not  will  be  found  to  belong 
to  each  of  the  two  parts  (Reason  and  Consequent)  taken 
separately ;  while  the  Sumption,  as  a  whole,  affirms  the 
connection  of  these  two  negative  parts  with  each  other. 

Agreeably  to  what  has  been  said,  a  Disjunctive  Syllogism 
is  one  of  which  the  Major  Premise  is  a  Disjunctive  Judg* 


CONDITIONAL  SYLLOGISMS.  213 

merit,  while  the  Minor  Premise  and  the  Conclusion  are  Cate- 
gorical Judgments.  The  Axiom  of  Excluded  Middle,  by 
which  this  sort  of  Syllogism  is  governed,  affirms  that,  of 
two  Contradictories,  one  must  be  true  and  the  other  must 
be  false.  Accordingly,  if  the  Major  Premise  presents 
three  or  more  Disjunct  Members,  the  Axiom  will  not  be 
immediately  applicable ;  these  three  or  more  Members  are 
only  Contraries  with  respect  to  each  other,  and  they  must 
be  reduced  to  two  Contradictories,  before  we  can  obtain  a 
ground  of  inference,  from  positing  or  sublating  one  of  them, 
to  sublating  or  positing  the  other.  The  number  of  such 
Members  can  always  be  thus  reduced  by  considering,  for 
the  moment,  two  or  more  of  them  as  one.  After  this  re- 
duction is  accomplished,  the  Minor  Premise  and  Conclusion 
appear  in  their  true  character,  not  as  Disjunctive,  but  as 
Categorical  Judgments.     For  example  :  — 


Complete  Formula. 

A  is  either  B,  C,  or  D ; 
But  A  is  neither  B  nor  C ; 
Then  A  is  D.* 


Reduced  Formula. 
Let  BorC=X. 

A  is  either  X  or  D ; 
But  A  is  .not  X  ; 
Then  A  is  D. 


This  formula,  as  reduced,  presents  the  universal  type  of 
Disjunctive  reasoning.  As  its  two  Disjunct  Members  are 
Contradictories  of  each  other,  the  Axiom  of  Excluded  Mid- 
dle authorizes  us,  from  positing  either  one  of  them,  to  sub- 
late  the  other.  This  is  called  the  Modus  ponendo  tollens, 
and  it  has  two  forms,  according  as  we  posit  one  or  the 
other  of  the  two  Disjunct  Members.     The  same  Axiom 

*  A  story  is  told  to  illustrate  the  sagacity  of  a  dog.  Following  his 
master  by  the  scent,  the  animal  came  to  a  place  where  three  roads  met,  *nd 
having  ascertained  by  his  nose,  at  two  of  them,  that  the  object  of  his  search 
had  not  taken  either  of  the  two,  he  immediately  darted  off  by  the  third,  with- 
out pausing  to  try  whether  this  path  also  was  scentless.  The  story  is  un- 
questionably a  fiction ;  but,  if  true,  the  dog  must  have  reasoned  by  this  form 
of  the  Disjunctive  Syllogism,  in  the  modus  tollendo  ponens. 


214  MEDIATE  INFERENCE  OR  SYLLOGISM. 

permits  us,  from  sublating  either  of  the  two,  to  posit  the 
other.  This  is  called  the  Modus  tollendo  ponens,  and  has 
two  forms  like  the  other.  Hence,  every  Disjunctive  Syllo- 
gism affords,  from  the  same  Major  Premise,  two  valid 
Moods,  each  containing  two  forms.  It  is  obvious,  that  the 
remaining  Term,  A,  of  the  Major  Premise,  may  be  quan- 
tified as  all  or  this,  and  the  Conclusion  will  appear  accord- 
ingly as  Universal  or  Singular.  The  two  Moods  and  four 
forms  of  a  Disjunctive  Syllogism  are  exhibited  in  the  fol- 
lowing example :  — 

Major  Premise.     Every  Judgment  is  either  Affirmative  or 
Negative. 

Modus  Ponendo  Tollens. 
Mr st  form.        This  Judgment  is  Affirmative ; 

Then  it  is  not  Negative. 
/Second  form.     This  Judgment  is  Negative ; 

Then  it  is  not  Affirmative. 
Modus  Tollendo  Ponens. 
First  form.        This  Judgment  is  not  Affirmative  ; 

Then  it  is  Negative. 
Second  form.     This  Judgment  is  not  Negative ; 

Then  it  is  Affirmative. 

For  those  who  are  fond  of  mnemonic  hexameters,  Ham- 
ilton has  presented  all  four  forms  in  the  following  verses :  — 

Ponendo  tollens.      Falleris  aut  fallor ;  fallor ;  non  fallen's  ergo. 

Falleris  aut  fallor ;  tu  falleris  ;  ergo  ego  nedum. 
Tollendo  ponens.     Falleris  aut  fallor ;  non  fallor ;  falleris  ergo. 

Falleris  aut  fallor ;  non  falleris ;  ergo  ego  fallor. 

Three  Special  Rules  have  been  framed  for  Disjunctive 
Syllogism,  though  they  are  so  obvious  that  their  formal 
enouncement  is  hardly  necessary. 

1.  A  regular  Disjunctive  Syllogism  must  consist  of 
three  Judgments  only,  in  which,  if  the  Major  Prem'se 
be   reduced    to   its    proper   logical    form,    there    can    be 


CONDITIONAL  SYLLOGISMS.  215 

only  three  Terms,  all  of  which  must  appear  in  the  Major 
Premise. 

2.  The  Major  Premise  must  be  Universal  and  Affirma- 
tive ;  the  Minor  Premise  may  be  of  either  Quality  and  of 
either  Quantity. 

3.  The  Conclusion  must  be  of  the  same  Quantity,  but  of 
opposite  Quality,  with  the  Minor  Premise. 

Agreeably  to  what  was  said  in  treating  of  Disjunctive 
Judgments,  each  Mood  of  a  Disjunctive  Syllogism  may  be 
resolved  into  a  Hypothetical  Syllogism,  and  then  its  two 
forms  appear  as  the  two  Moods  of  the  Hypothetical  reason- 
ing. For  instance,  the  example  last  cited  may  be  thus 
transformed :  — 

If  any  Judgment  is  not  Affirmative,  it  is  Negative. 

Modus  Ponens.  Modus  Tollens. 

This    Judgment   is  not  Af-     This  Judgment  is  not  Neg- 

ftrmative  ;  ative ; 

Then  it  is  Negative.  Then  it  is  Affirmative. 

As  a  Dilemmatic  Syllogism  consists  of  a  Hypothetical 
and  a  Disjunctive  combined,  and  as  these  two  may  be  com- 
bined in  several  different  ways,  the  resulting  forms  are 
numerous  and  complex.  Most  of  them  are  really  com- 
pound, and  a  full  analysis  would  need  to  resolve  them 
into  several  simple  and  subordinate  Syllogisms.  It  would 
be  tedious  to  analyze  them  all,  and  this  is  not  necessary, 
as  the  principles  already  established  for  the  Hypothetical 
and  the  Disjunctive  Syllogisms  taken  separately,  still  gov- 
ern them  when  taken  in  connection;  and  the  learner  in 
each  case  may  make  the  analysis  and  apply  the  principles 
for  himself.  What  follows  is  to  be  regarded  only  as  illus- 
trating the  method  to  be  pursued. 

What  has  already  been  presented  as  a  type  of  the  Di- 
lemmatic Syllogism  is,  in  fact,  only  a  Hypothetical  dis- 
guised, as  the  Disjunction  is  not  resolved,  and  therefore  its 


216  MEDIATE  INFERENCE   OR   SYLLOGISM. 

Disjunct  Members,  whether  two  or  more,  may  be  regarded 
as  a  single  Term. 

If  A  is  B,  C  is  either  D  or  E. 

Modus  Pojjens.  Modus  Tollens. 

But  A  is  B  ;  C  is  neither  D  nor  E  ; 

.\  C  is  either  D  or  E.         .\  A  is  not  B. 

In  practice,  however,  the  Disjunction  is  usually  resolved^ 
in  the  Modus  tollens,  by  two  subordinate  (abridged)  Syllo- 
gisms, by  which  it  is  first  separately  proved  that  C  is  not  D, 
and  that  C  is  not  E ;  and  then  the  Conclusion  of  the  com- 
pound Modus  tollens  follows,  that  A  is  not  B.     Thus :  — 

If  man  cannot  be  virtuous,  either  he  must  be  unable  to 
know  what  is  right,  or  unable  to  will  what  is  right. 

But  he  is  not  unable  to  know  what  is  right,  for  he  is  in- 
telligent; and  he  is  not  unable  to  will  what  is  right, 
for  he  is  free. 

Therefore,  he  can  be  virtuous. 

Hence,  the  Dilemma  was  called  by  the  old  logicians 
the  Cornutus  or  horned  syllogism,  because,  in  the  Sump- 
tion, the  Disjunct  Members  are  opposed  like  horns  to  the 
assertion  of  the  adversary ;  with  these,  we  throw  it  from 
one  side  to  the  other  in  the  Subsumption,  in  order  to  toss 
it  altogether  away  in  the  Conclusion. 

Krug  remarks :  u  The  Cornutus  and  Crocodilinus  of  the 
ancients  must  not  be  confounded  with  the  Dilemma  which 
we  are  here  speaking  of.  The  former  were  sophismata 
heterozeteseos,  sophisms  of  counter-questioning ;  the  latter  is 
a  legitimate  mode  of  reasoning."  But  it  may  be  shown 
that  the  old  Cornutus  is  a  legitimate  Dilemma  in  Form, 
and  is  of  the  type  which  we  are  now  considering,  the  fal- 
lacy being  in  the  Matter.  The  IAtigiosus,  for  instance, 
which  is  one  illustration  of  this  old  fallacy,  may  be  thus 
resolved. 


CONDITIONAL   SYLLOGISMS.  21  [ 

Protagoras  agreed  for  a  large  sum  to  educate  Euathlus 
as  a  lawyer,  one  half  of  the  price  to  be  paid  down,  and 
the  other  half  on  the  day  when  the  pupil  should  plead  and 
gain  his  first  cause.  Some  time  elapsed,  and  Protagoras, 
thinking  that  his  disciple  intentionally  delayed  the  com- 
pletion of  his  contract,  sued  him  in  court  for  the  remainder 
of  the  fee,  and  propounded  this  Dilemma. 

If  Euathlus  is  to  be  released  from  the  payment  of  this 
sum,  it  must  be  either  because  the  judgment  of  this  court 
will  be  in  his  favor,  or  against  him. 

But  if  the  judgment  is  in  his  favor,  then  he  has  pleaded 
and  gained  his  first  cause,  and  the  money  is  due  me  under 
the  contract. 

If  the  judgment  is  against  him,  the  money  is  due  me 
under  the  decision  of  the  court. 

Thus,  both  the  Disjunct  Members  of  the  Consequent 
being  disproved  by  subordinate  Syllogisms,  the  Conclusion 
of  the  compound  Modus  tollens  follows,  that  Euathlus  is 
not  to  be  released  from  the  payment. 

The  Dilemma  is  here  correct  in  Form,  but  there  is  a 
Material  Fallacy  in  the  Major  Premise,  since  the  Disjunc- 
tion is  not  complete.  There  is  a  third  horn  to  it,  as  Pro- 
tagoras had  no  right,  under  the  contract,  to  invoke  the 
judgment  of  the  court  at  all,  so  that  the  judges  ought  to 
have  dismissed  the  case  without  a  hearing.  Before  a  judg- 
ment was  rendered,  Protagoras  had  no  ground  of  action. 

Euathlus  is  said  to  have  retorted  upon  his  antagonist,  by 
propounding  a  Dilemma  in  the  same  Form  in  which  it  had 
just  been  urged  against  him.  "  If  the  decision  be  favor- 
able to  me,  I  shall  pay  nothing  under  the  sentence  of  the 
court ;  if  adverse,  I  pay  nothing  in  virtue  of  the  compact, 
because  I  shall  not  have  gained  my  first  cause." 

•"  In  sifting  a  proposed  Dilemma,"  says  Krug,  "  we  are 
to  look  closely  to  the  three  following  particulars :  — 
1.  Whether,  in  the  Sumption,  the  Consequent  is  a  legiti- 
10 


218  MEDIATE  INFERENCE   OR   SYLLOGISM. 

mate  inference  from  the  Antecedent;  2.  Whether  the 
Disjunction  in  the  Consequent  is  complete ;  3.  Whether, 
in  the  Subsumption,  the  Disjunct  Members  are  properly 
sublated.  The  following  Dilemma  is  faulty  in  each  of 
these  respects. 

"  If  Philosophy  be  of  any  value,  it  must  procure  for  u* 
power,  riches,  or  honor. 

"  But  it  procures  neither  of  them.  Therefore,  &c. 
"  Here,  1.  the  inference  is  wrong,  as  Philosophy  may  be 
worth  something,  though  it  does  not  secure  any  of  these 
external  advantages;  2.  the  Disjunction  is  incomplete,  as 
there  are  other  goods,  besides  the  three  here  enumerated ; 
3.  the  Subsumption  is  false,  as  Philosophy  has  often  been 
the  means  of  procuring  these  very  advantages." 

In  another  form  of  the  Dilemma,  the  Sumption  is  a 
Hypothetical  Judgment  with  more  than  one  Antecedent, 
and  the  Subsumption  is  a  Disjunctive  of  which  these  sev- 
eral Antecedents  are  the  Disjunct  Members. 

If  A  is  B,  C  is  D  ;  and  if  E  is  F,.C  is  D; 
But  either  A  is  B  or  E  is  F ; 
.-.  C  is  D. 
Here,  the  several  Antecedents  have  the  same  Conse- 
quent, and  therefore  the  Conclusion  is  Categorical.      If 
they  had  different  Consequents,  the  Conclusion  would  be 
Disjunctive.     Thus :  — 

If  A  is  B,  C  is  D  ;  and  if  E  is  F,  G  is  H ; 
But  either  A  is  B  or  E  is  F  ; 
.-.  Either  C  is  D,  or  G  is  H. 
In  this  case,  the  Modus  tollens  is  also  valid ;  if  we  dis- 
junctively deny  the  Consequents,  we  may,  in  the  Conclu- 
sion, disjunctively  deny  the  Antecedents. 

Either  C  is  not  D,  or  G  is  not  H. 
.*.  Either  A  is  not  B,  or  E  is  not  F. 
In  the  preceding  case,  where  the  Antecedents  had  the 


DEFECTIVE  AND   COMPLEX   SYLLOGISMS.  219 

same  Consequent,  if  we  deny  this  one  Consequent,  we  must 
deny  the  Antecedents  taken  collectively,  and  not  disjunc- 
tively ;  then  the  Syllogism  will  be  exclusively  Hypotheti- 
cal, as  neither  Judgment  will  be  disjunctive.     Thus  :  — 

If  A  is  B,  C  is  D  ;  and  if  E  is  F,  C  is  D  ; 

But  C  is  not  D  ; 
.*.  Then  A  is  not  B,  and  E  is  not  F. 
The  nature  of  a  Disjunction  is,  that  any  one  of  the  Dis- 
junct Members  exists,  or  is  posited,  only  by  the  non-exist- 
ence, or  sublation,  of  all  the  others.  Hence,  the  particles, 
either — or,  have  a  Disjunctive  force;  but  the  corresponding 
negative  particles,  neither  —  nor,  have  a  Conjunctive  force, 
as  they  denote  the  exclusion  of  both  or  all,  and  not  merely 
the  exclusion  of  one  on  condition  of  the  inclusion  of  all  the 
others.  A  is  either  B  or  C,  means  that  A  is  B  only  on  con- 
dition that  A  is  not  0.  But  A  is  neither  B  nor  C,  means 
that  A  is  not  B  and  is  not  Q. 

It  has  been  remarked,  that  the  Modus  tollens  of  the  Di- 
lemma, in  the  form  in  which  it  was  here  first  proposed,  is 
nothing  but  a  Negative  induction. 

If  A  is  B,  C  is  either  D,  E,  or  F ; 

But  C  is  neither  D,  E,  nor  F ; 

Then  A  is  not  B. 
This  can  be  resolved  into   a  Categorical  Syllogism  of 
Induction.     Thus :  — 

C  is  not  D,  is  not  E,  and  is  not  F ; 

But  these  are  all  the  possible  cases  of  A  being  B  ; 

Then  A  is  not  B. 

3.    Defective  and  Complex  Syllogisms. 

It  has  already  been  mentioned,  that  men  do  not  usually 
speak  or  write  complete  Syllogisms  ;  nay,  it  is  almost  only 
in  treatises  on  Logic  that  we  find  Syllogisms  completely 


220  MEDIATE  INFERENCE   OR  SYLLOGISM. 

enounced,  or  with  all  their  parts  expressed.  ■  The  abridged 
form  is  preferred  on  all  ordinary  occasions,  because  at  least 
one  of  the  three  Judgments  is  so  obvious,  both  to  the 
speaker  and  the  hearer,  that  it  would  be  a  waste  of  time 
and  words  —  a  sin  against  brevity,  and  even  against  per- 
spicuity—  to  propound  it  openly;  for  unnecessary  words 
do  not  elucidate,  but  obscure,  the  Thought.  We  usually 
express  a  single  process  of  reasoning  by  two  Judgments, 
connected  by  an  illative  particle,  because,  then,  therefore, 
&c. ;  sometimes  only  by  a  conjunctive  particle,  and.  The 
following  are  instances  of  reasoning  thus  enounced. 

Aldebaran  is  a  star ;  therefore,  it  shines  by  its  own  light. 
No  avaricious  person  can  be  happy ;  because  he  who  is 

never  free  from  fear  cannot  be  happy. 
A  liar  ought  not  to  be  believed ;  and  this  witness  has  been 

proved  to  be  a  liar. 

Such  sentences  as  these  are  called  Enthymemes,  because 
they  are  abridged  statements  of  a  process  of  reasoning,  one 
of  the  three  Judgments  necessary  to  constitute  the  Syllo- 
gism being  ev  6v/jlw,  in  the  mind,  but  not  expressed.  In 
the  first  case,  the  suppressed  Judgment  is  the  Major  Prem- 
ise, —  all  stars  shine  by  their  own  light ;  in  the  second,  it 
is  the  Minor  Premise,  —  an  avaricious  person  is  never  free 
from  fear,  the  Conclusion  also,  as  is  frequently  the  case  in 
.Enthymemes,  being  placed  first,  instead  of  last ;  in  the 
third  case,  the  suppressed  Judgment  is  the  Conclusion, — 
this  witness  ought  not  to  be  believed. 

An  Enthymeme,  then,  is  not  a  peculiar  kind  of  Syllo- 
gism, but  only  an  abridged  expression  of  a  Syllogism.  Of 
course,  the  doctrine  of  Enthymemes  properly  belongs,  not 
to  Logic,  but  to  Rnetoric,  for  it  concerns  expression,  not 
thought ;  and  it  would  never  have  been  obtruded  into  the 
former  science  but  for  the  authority  of  Aristotle,  who  em- 
ployed the  name>  indeed,  in  a  different  and  now  disused 


DEFECTIVE  AND  COMPLEX  SYLLOGISMS.       221 

meaning,  signifying  by  it  "  a  reasoning  from  signs  and  like- 
lihoods." 

Hitherto,  we  have  treated  only  of  the  so-called  Mono- 
syllogism, —  that  is,  of  a  Syllogism  considered  as  one  in- 
dependent whole,  without  reference  to  the  continuous  chain 
of  reasoning,  of  which,  in  an  abridged  form  of  expression, 
it  usually  constitutes  a  single  link.  Many  truths  —  most 
of  the  theorems  in  Geometry,  for  instance  —  can  be 
proved  only  by  a  Chain  of  Reasoning ;  —  that  is,  by  a 
connected  series  of  Syllogisms,  the  several  portions  of 
which  are  dependent  upon  each  other.  A  Conclusion  of 
one  may  become  a  Premise  of  the  next  succeeding  Syllo- 
gism, and  is  then  called,  in  reference  to  its  successor,  a 
Prosyllogism ;  while  the  latter,  in  reference  to  the  one 
which  preceded  it,  is  called  an  Episyllogism.  A  Prosyllo- 
gism, then,  is  a  Syllogism  whose  Conclusion  is  a  Premise  of 
that  which  follows  ;  and  an  Episyllogism  is  one  whose  Prem- 
ise is  a  Conclusion  of  that  which  precedes.  As,  in  a  hierarchy 
of  Concepts,  the  same  class-notion  is  at  once  a  Genus  to 
the  class  below  and  a  Species  to  the  class  above ;  so,  in  a 
Chain  of  Reasoning,  the  same  Syllogism  is  at  once  a  Pro- 
syllogism  and  an  Episyllogism  in  its  opposite  relations. 
Only  that  which  contains  the  primary  or  highest  reason 
can  be  exclusively  called  a  Prosyllogism ;  only  that  which 
enounces  the  last  or  lowest  consequent  is  exclusively  an 
Episyllogism. 

The  Syllogism  constituting  a  Chain  may  be  either  partly 
complete  and  partly  abbreviated,  or  all  equally  abbreviated. 
In  the  former  case,  the  complex  Syllogism  which  results  is 
called  an  Epicheirema ;  in  the  latter,  it  is  called  a  Sorites. 

A  Syllogism  is  called  an  Epicheirema,  when,  to  either  or 
both  of  its  two  Premises,  there  is  attached  a  reason  for  its 
support.  The  Premise  with  such  a  rider  annexed  is,  in 
fact,  a  Prosyllogism  abbreviated,  —  that  is,  an  Enthymeme 
used  to  prove  one  of  the  branches  of  the  main  Syllogism. 
Thus :  — 


222  MEDIATE  INFERENCE   OR  SYLLOGISM. 

M  is  P ;  The  flesh  of  ruminants  is  good  fof 

food ; 
S  is  M,  because  it  is  N ;        These  animals  are  ruminants,  be- 
cause they  have  cloven  hoofs  ; 
\  S  is  P.  .*.  These  animals  are  good  for  food. 

Here,  the  Enthymeme,  which  is  a  rider  of  the  Minor 
Premise,  may  be  thus  explicated  into  a  complete  Prosyllo- 
gism. 

All  animals  which  have  cloven  hoofs  are  ruminant ; 
These  animals  have  cloven  hoofs  ; 
.\  These  animals  are  ruminants. 

It  has  already  been  said,  that  every  Syllogism  may  be 
regarded  as  an  application  of  the  general  and  self-evident 
principle,  that  a  part  of  a  part  is  a  part  of  the  whole.  If,  in 
the  application  of  this  principle,  we  do  not  stop  at  the  first 
or  proximate  whole,  but,  before  drawing  any  expressed  Con- 
clusion, proceed  step  by  step  to  remoter  parts  and  more 
comprehensive  wholes,  and,  in  the  Conclusion,  finally  place 
the  smallest  part  under  the  largest  whole,  the  complex 
abbreviated  reasoning  thus  formed  is  called  a  Chain-Syllo- 
gism, or  Sorites.  It  may  be  aptly  symbolized  by  a  series 
of  concentric  ciicles. 


1.  A  is  B ; 

2.  BisC; 

3.  C  is  D  ; 

4.  D  is  E  ; 
Therefore,  A  is  E. 


A  Sorites  of  this  sort  may  be  described  as  a  series  of 
Enthymemes  with  suppressed  Conclusions,  in  which  the  Pred- 
icate of  each  is  the  Subject  of  the  next,  and  the  Conclusion 
of  the  whole  is  formed  from  the  first  Subject  and  last  Pred- 
icate of  the  Premises.     The  Conclusion  being  thus  formed, 


DEFECTIVE  AND   COMPLEX  SYLLOGISMS.  223 

it  is  evident  that  there  must  be  as  many  Middle  Terms 
(i.  e.  Terms  intervening  between  the  first  Subject  and  last 
Predicate,  that  is,  again,  between  the  smallest  part  and  the 
greatest  whole  which  the  reasoning  connects)  as  there  are 
Premises  minus  one ;  consequently,  every  Sorites  may  be 
explicated  into  as  many  distinct  Syllogisms  as  there  are 
Premises  minus  one.  The  first  Judgment  in  the  Sorites  is 
the  only  Minor  Premise  that  is  expressed ;  each  of  the 
other  Minor  Premises  is  the  Conclusion  of  the  separate 
Syllogism  next  preceding.  Hence,  each  of  the  Judgments 
in  the  Sorites  except  the  first  is  the  Major  Premise  of  a 
distinct  Syllogism.  The  preceding  Sorites,  for  instance, 
may  be  thus  explicated  into  three  Syllogisms,  the  correct- 
ness of  the  explication  being  made  very  evident  by  a  refer- 
ence to  the  diagram. 


I. 

ii. 

in. 

2.  B  is  C, 

3.  C  is  D, 

4.  D  is  E, 

1.  A  is  B  ; 

A  is  0; 

A  is  D  ; 

.-.  a  is  a 

.-.  A  is  D. 

.-.  A  is  K 

An  invalid  Mood  occurring  anywhere  in  the  series 
before  the  last  Syllogism  would  not  only  be  wrong  itself, 
but,  as  furnishing  a  Premise  to  its  successors,  would  vitiate 
all  that  follow.  Hence,  in  a  Sorites,  out  of  all  the  Prem- 
ises, only  the  one  first  expressed  may  be  Particular ;  be- 
cause, in  the  First  Figure,  to  which  all  the  separate  Syllo- 
gisms belong,  the  Minor  Premise  may  be  Particular,  but 
not  the  Major;  and  all  the  Judgments  in  the  Sorites, 
except  the  first  and  the  Conclusion,  are  Major  Premises. 
In  the  Sorites,  also,  only  the  last  Judgment  may  be  Nega- 
tive ;  for  if  any  other  of  its  Judgments  were  Negative,  the 
Syllogism  formed  from  the  next  following  Judgment  would 
have  a  Negative  Minor  Premise,  which  the  First  Figure 
does  not  admit.  A  Sorites  in  the  Modus  tollens,  then,  can 
be  stated  only  in  one  form ;  —  from  denying  the  last  Con- 


224  MEDIATE  INFERENCE   OR  SYLLOGISM. 

sequent  of  the  last  Antecedent,  we  go  back  to  denying 
this  same  Consequent  of  the  first  Antecedent.  Thus,  if 
we  say  that  D  is  not  E,  we  must  conclude  that  A  is  not  E. 
The  three  distinct  Syllogisms  already  given  are  not  all 
that  may  be  formed  from  the  given  Sorites.  Instead  of  be- 
ginning with  the  first  Judgment,  and  thereby  finally  con- 
cluding that  A  is  E,  we  may  begin  with  the  second  Judg- 
ment, first  concluding  that  B  is  D,  and  then  that  B  is  E , 
and  again,  beginning  with  the  third,  we  may  conclude  that 
C  is  E.  Hence,  from  a  Sorites  with  four  Premises,  we 
may  form  in  all  six  distinct  Syllogisms.  If  there  were  five 
Premises,  there  would  be  ten  resultant  Syllogisms.  "  The 
formula,"  says  Dr.  Thomson,  "  for  ascertaining  the  num- 
ber of  Conclusions  is  this :  — -  Let  the  number  of  Premises 
ex  n ;  the  number  of  terms  =  n  -f-  1 ;  then  the  number 

of  Conclusions  =  —        — — 

Goclenius  invented  another  form  of  the  Sorites,  to  which 
his  name  has  been  attached  ;  it  is  the  same  as  the  common 
form,  except  that  the  Premises  are  reversed.  Referring  to 
the  diagram  again,  it  is  evident  that,  instead  of  beginning 
with  the  Terms  of  least  Extension,  represented  by  the  in- 
nermost circles,  we  may  begin  with  the  more  Extended 
Terms  in  the  outer  circles.  Then  the  Subject  of  each 
Judgment  becomes  the  Predicate  of  the  next;  while,  in 
.the  common  form,  it  is  the  Predicate  of  the  former  which 
becomes  the  Subject  of  the  latter.  The  Goclenian  Sorites 
is  thus  stated :  — 

DisE, 

CisD, 

BisC, 

AisB; 
.-.  A  is  E. 

Here,  Extension  is  more  prominent,  as  we  start  with  the 
wider  Terms ;  hence,  this  form  is  better  suited  for  deduc- 


DEFECTIVE  AND  COMPLEX  SYLLOGISMS.       225 

tion.  In  the  common  form,  Intension  predominates,  as 
the  narrower  Terms  come  first;  Induction  naturally  as- 
sumes this  Form. 

"  A  '  pretty  quarrel '  long  existed  amongst  logicians," 
says  Dr.  Thomson,  "  which  of  the  two  was  to  be  called 
progressive  and  which  regressive.  It  was  a  mere  strife 
about  words.  If  we  are  discovering  truth  by  the  inductive 
method,  the  Aristotelian  form  is  progressive  ;  if  we  are 
teaching  truth,  or  trying  our  laws  upon  new  facts,  we  use 
deduction,  and  the  Goclenian  form  is  progressive.  In  an 
apt  but  familiar  figure,  —  if  I  am  on  the  ground  floor,  and 
wish  to  fetch  something  that  is  above,  my  going  up  stairs  is 
my  progress  towards  my  object,  and  my  coming  down  is  a 
regression ;  if  the  positions  of  myself  and  the  thing  are  re- 
versed, going  down  would  be  progress,  and  returning  up, 
regress.  The  inductive  truth-seeker  is  on  the  ground-floor 
of  facts,  and  goes  up  to  seek  a  law ;  the  deductive  teacher 
is  on  a  higher  story,  and  carries  his  law  down  with  him  to 
the  facts. 

"  This  will  be  clearer  from  a  pair  of  examples. 

Goclenian  or  descending  Sorites.  Aristotelian  or  ascending  Sorites. 

Sentient  beings  seek  happiness  ;      Caius  is  a  man ; 
All  finite  beings  are  sentient ;         All  men  are  finite  beings  ; 
All  men  are  finite  beings ;  All  finite  beings  are  sentient ; 

Caius  is  a  man ;  All  sentient  beings  seek  happi- 

ness ; 
Therefore    Caius   seeks   happi-     Therefore  Caius   seeks  happi- 
ness, ness." 

By  way  of  recapitulation,  the  chief  principles  and  rules 
of  the  Aristotelic  doctrine  of  Syllogism  are  brought  to- 
gether in  the  following  Conspectus. 


10 


226 


CONSPECTUS   OF   THE   ARISTOTEL1C 


Mediate  Inference  ok  Syllo- 
gism 

is  that  act  of  Thought  whereby  the 
relation  of  the  two  Terms  of  a  pos- 
sible Judgment  to  each  other  is 
ascertained  by  comparing  each  of 
them  separately  with  a  Third  Term. 


Syllogisms 

Categorical. 

in  which  each  of  the  three  Jiulgments  can  be 
expressed  under  one  or  the  other  of  these 
two  Formulas :  — 

A  is  B  :  A  is  not  B. 


General  Canom 

of  Categorical  Syllogisms.  In  so  far 
as  two  Notions,  (Concepts  or  Indi- 
viduals,) either  both  agree,  or,  one 
agreeing,  the  other  does  not  agree, 
with  a  common  Third  Notion,  in 
so  far  these  Notions  do,  or  do  not, 
agree  with  each  other. 


This  Canon  is  explicated 
H. 


A  Syllogism  must 
contain  three  Terms, 
and  no  more. 


A  Syllogism  must 
contain  three  Judg- 
ments, and  no  more. 


The  Figure 

of  a  Syllogism  is  determined  by  the 
relative  position  of  the  Middle  Term 
in  the  two  Premises. 


LetS -Subject  of  the 


Figure  I.  MP: 
SM; 
.-.  S  P. 


The  Mood 

of  a  Syllogism  is  the  value  of  its  three 
Judgments  in  respect  to  their  Quan- 
tity and  Quality,  as  indicated  in 
each  case  bv  the  four  Judgments, 
A,  E,  I,  and  O. 


Valid 


Fig.  I. 
AAA;  Barbara. 
E  A  E  ;  Celarent. 
All;  Darii. 
E  I  O  ;  Ferio. 


Reduction 

of  the  valid  Moods  of  the  three  lower 
Figures  to  those  of  the  First  Fig- 
ure may  be  accomplished  by  per- 
forming the  processes  indicated  by 
the  following  letters  in  the  names 
of  those  Moods. 


B  =  Reduce  the  Mood  to  Barbara. 
C  =»  "  "  Celarent. 

D  =  "  "  Darii. 

F-         «  «  Ferio 


General  Canon 

of  Hypothetical  Syllogisms.  To  affirm 
the  Reason  or  the  Condition  is  to 
affirm  the  Consequent ;  and  to  deny 
the  Consequent  is  also  to  deny  the 
Reason. 


This  Canon  produces,  from 

Major  Precise 

Modus  Ponens. 
AisB: 
.-.  C  is  D. 


General  Canon 

of  Disjunctive  Syllogisms.  Of  two 
Contradictories,  one  must  be  true 
and  the  other  must  be  false. 


This  Canon  produces,  Yom 
Major  Pre  <nw«, 


Modus  ponendo  tollens. 

1.  AisB; 

.-.  A  is  not  C. 

2.  A  is  C  ; 

.-.  A  is  not  B. 


DOCTRINE   OF  SYLLOGISM. 


227 


ABB   EITHER 


ob  Conditional,  - 


in  which  the  Major  Premise,  and  only  the  Major  Premise,  is  a  Conditional  Judgment ;  *nd 
these  are  subdivided  into 


Hypothetical  i 
Major  Premise, 
If  A  is  B,  CisD. 


Disjunctive  ; 
Major  Premise, 
A  is  either  B  or  C. 


Dilemmatic  or  Hypotheti- 
cal Disjunctive. 
Major  Premise, 
If  A  is  B,  C  is  either  D  or  E. 


mto  these  six  General  Rules. 

in. 


The  Middle  Term 
must  be  distributed 
in  at  least  one  of  the 
Premises. 


IV. 


One  Premise  at  least 
must  be  Affirmative. 


If  either  Premise  is 
Negative,  the  Con- 
clusion must  be  Neg- 
ative. 


VI. 

Neither  Term  must 
be  distributed  in  the 
Conclusion,  if  it  was 
not  distributed  in 
the  Premise. 


Conclusion  : 


Figure  II.  P  M  ; 
SM; 
.-.  S  P. 


P  =  Predicate  of  the  Conclusion ;  M  m  Middle  Term.    Then 

Figure  IV. 


Figure  III.  M  P  ; 
MS; 
.-.  S  P. 


PM| 
MS} 
.8P 


Moods. 

Fig.  n. 

EAE;  Cesare. 
ABE;  Camestres. 
E  I  O  5  Festino. 
AOO;   Baroko  (Fakoro). 
All  Negative  Conclusions. 


Fig.  m. 

A  A  I ;  Darapti. 
I  A  I ;  Disamit. 
All;  Datisi. 
E  A  O  ;  Felapton. 
O  A  O  ;  Bokardo  (Dokamok). 
E  I  O.  Ferison. 
All  Particular  Conclusions. 


Fig.  IV. 
A  A  I ;  Bramantip. 
A  E  E  ;  Camene%. 
I  A  I  ;  Dimari$. 
E  A  O  ;  Fesapo. 
E  I  O  ;  Fresison. 


m  «=  Transpose  the  Premises 
$  ■=  Convert  simply. 
p  =  Convert  per  accidens. 
k  =  Reduce  per  impossibile   for 

Baroko  k  Bokardo  ; 
Convert  by  Contraposition  for 

Fakoro  &  Dokamok. 


Barbara,  Celarent,  Darii,  Fer toque,  prloris  j 
Cesare,  Camestres,  Festino,  Baroko,  secundae  , 
Tertia  Darapti,  Disamis,  Datisi,  Felapton, 
Bokardo,  Ferison  habet ;  Quarta  insuper  addit 
Bramantip,  Camenes,  Dimaris,  Fesapo,  Fresison, 


the  same  Premise,  two  valid  Moods. 
If  A  is  B,  CisD. 

Modus  Tollens. 

C  is  not  D  ; 
A  A  is  not  B. 


the  same  Premise,  two  valid  Moods,  each  having  two 

A  is  either  B  or  C. 

Modus  tollendo  ponens. 
1.       A  is  not  B  ; 

.«.  A  is  C. 
3.      A  is  not  C  ; 

-•  A  is  B. 


228  MEDIATE   INFERENCE   OR   SYLLOGISM 


CHATTER   VIII. 

THE  HAMILTONIAN  DOCTRINE   OF  SYLLOGISMS. 

SIR  William  Hamilton's  innovations  in  the  doctrine 
of  Syllogisms,  which  had  been  generally  received 
up  to  this  time,  are  not  limited  to  such  as  are  the  direct 
consequences  of  his  theory  of  the  thorough-going  quanti- 
fication of  the  Predicate.  On  several  minor  points,  also, 
he  has  considerably  modified  the  Aristotelic  doctrine. 
These  changes,  it  is  true,  were  probably  suggested  by  his 
system  of  quantifying  the  Predicate ;  but  they  are  not  so 
closely  connected  with  it  as  to  prevent  them  from  being 
received,  even  by  those  logicians  who,  wholly  or  in  part, 
reject  that  system.  All  of  them  deserve  consideration,  as 
they  involve  a  discussion  of  some  incidental  questions  of 
much  interest,  affecting  the  whole  theory  of  Logic. 

As  to  the  order  of  enouncement,  the  old  doctrine  was, 
that  the  Premises,  as  their  name  imports,  should  precede 
the  Conclusion.  Hamilton  observes  that  the  reverse  order 
is  more  natural,  that  it  more  faithfully  represents  the 
progress  of  the  mind  in  the  investigation  or  discovery  of 
truth,  and  that  it  effectually  relieves  the  Syllogism  from 
the  imputation,  which*  has  been  thrown  upon  it  for  more 
than  three  centuries,  of  being  founded  upon  a  mere  petitio 
pincipii,  or  a  begging  of  the  question.  "  Mentally  one," 
he  says,  "  the  Categorical  Syllogism,  according  to  its  order 
of  enouncement,  is  either  Analytic,  if  what  is  inappro- 
priately styled  the  •  Conclusion '  be  expressed  first,  and 
what  are  inappropriately  styled  the    *  Premises '   be  then 


THE  HAMILTONIAN  ANALYSIS.  229 

stated  as  its  reasons  ;  or  Synthetic,  if  the  Premises  precede 
and,  as  it  were,  effectuate  the  Conclusion. "  In  the  Ana- 
lytic order,  the  "  Conclusion  "  would  be  more  properly 
called  the  Qucesitum,  and  the  "Premises"  should  be 
denominated  the  Proofs. 

Now,  the  Analytic  order,  it  is  argued,  is  the  more  nat- 
ural, because  the  Problem  or  Question,  which  it  is  the 
purpose  of  the  Syllogism  to  solve  or  answer,  and  which  is 
therefore  the  leading  thought  in  the  mind,  is  propounded 
first.  When  we  are  in  doubt  whether  A  is,  or  is  not,  B, 
it  is  surely  more  natural  to  argue,  A  is  B,  because  A  is  (7, 
and  all  0  is  B,  than  to  reason  in  the  old  order,  placing  the 
solution  of  the  Problem  last  "  In  point  of  fact,  the^Ana- 
lytic  Syllogism  is  not  only  the  more  natural,  it  is  even  pre- 
supposed  by  the  Synthetic.'*  As  already  stated,  the  Syllo- 
gistic process  in  the  mind  is  really  one  and  undivided,  con- 
sisting only  in  the  inference  of  the  Conclusion  from  the 
Premises.  But  in  order  to  state  this  single  process  in 
words,  we  must  analyze  it,  and  therefore  the  Conclusion, 
which  is  the  compound  result,  ought  to  be  stated  first,  so 
as  to  admit  of  analysis.  It  may  be  stated  generally,  that  a 
process  of  investigation  or  research,  looking  towards  truth 
not  yet  discovered,  is  always  Analytic.  The  most  that  can 
be  said  for  the  Synthetic  method  is,  that  it  may  be  suc- 
cessfully used  for  teaching,  or  proving  the  truth  that  is 
already  known.  To  adopt  an  old  illustration,  in  order  to 
find  out  for  ourselves  how  a  clock  is  made  and  how  it  does 
its  work,  we  must  take  it  to  pieces ;  having  done  this,  the 
best  way  to  teach  another  person  how  to  make  a  clock  is 
to  take  those  pieces  and  put  them  together  again. 

The  common  objection  to  the  validity  of  the  Syllogistic 
process  is,  that  the  Conclusion  is  virtually  contained  in  the 
Premises,  so  that  we  have  to  assume  it  to  be  true  in  the 
very  propositions  by  which  we  attempt  to  prove  it.  This 
objection  is  thus  forcibly  stated  by  Mr.  Mill.  "  When  we 
say,  — 


230  MEDIATE  INFERENCE   OR   SYLLOGISM. 

All  men  are  mortal ; 

Socrates  is  a  man  ; 

Therefore,  Socrates  is  mortal ; 
it  is  unanswerably  urged  by  the  adversaries  of  the  Syllo- 
gistic theory,  that  the  proposition,  •  Socrates  is  mortal,'  is 
presupposed  in  the  more  general  assumption,  •  All  men 
are  mortal ' ;  that  we  cannot  be  assured  of  the  mor- 
tality of  all  men,  unless  we  were  previously  certain  of 
the  mortality  of  every  individual  man  ;  that  if  it  be  still 
doubtful  whether  Socrates,  or  any  other  individual  you 
choose  to  name,  be  mortal  or  not,  the  same  degree  of  un- 
certainty must  hang  over  the  assertion,  '  All  men  are 
mortal ' ;  that  the  general  principle,  instead  of  being  given 
as  evidence  of  the  particular  case,  cannot  itself  be  taken 
for  true  without  exception,  until  every  shadow  of  doubt 
which  could  affect  any  case  comprised  with  it  is  dispelled 
by  evidence  aliunde ;  and  then,  what  remains  for  the  Syl- 
logism to  prove  ?  that,  in  short,  no  reasoning  from  generals 
to  particulars  can,  as  such,  prove  anything :  since,  from  a 
general  principle,  you  cannot  infer  any  particulars  but  those 
which  the  principle  itself  assumes  as  foreknown." 

But  if  the  Syllogism  be  stated  in  the  Analytic  form, 
it  is  obvious  that  this  objection  is  inapplicable.  When  we 
argue,  — 

Socrates  is  mortal, 

Because  Socrates  is  a  man, 

And  all  men  are  mortal,  — 
we  do  not  assume  the  point  which  ought  to  be  proved,  but 
we  prove  that  it  is  right  to  predicate  mortality  of  Socrates, 
by  showing  that  Socrates  belongs  to  the  class  man,  all  the 
members  of  which  are  universally  admitted  to  be  mortal. 
We  appeal  to  the  admitted  Universal  truth  only  after  we 
have  established,  what  is  here  the  main  point  of  the  argu- 
ment, the  applicability  of  the  truth  to  this  case,  —  the  fact 
that  Socrates  is  a  man.     Mr.  Mill  mistakes  'the  compara- 


THE  HAMILTONIAN  ANALYSIS.  231 

tive  importance  of  the  two  Premises ;  in  Analytic  reason- 
ing, —  in  drawing  an  inference  for  the  purpose  of  investi- 
gation or  discovery,  —  the  proof  turns  chiefly  upon  the 
Subsumption ;  and  Aristotle  therefore  correctly  places  this 
Premise  first.  Thus,  if  I  am  in  doubt  with  respect  to  a 
new  substance  which  I  have  found,  whether  it  be  fusible  or 
not,  the  doubt  may  be  resolved  by  ascertaining  that  this 
substance  is  a  metal.  Only  after  this  fact  is  ascertained, 
and  then  only  in  order  to  complete  the  thought,  or  to  si- 
lence cavil,  I  refer  to  the  admitted  truth  that  all  metals  are 
fusible.  Men  usually  reason  in  this  manner,  as  is  shown 
by  the  frequent  recurrence  of  such  Enthymemes  as  these : 
This  iron  is  not  malleable,  for  it  is  cast-iron  ;  The  man  is 
dishonest,  for  he  has  taken  what  is  not  his  own ;  this  line  is 
equal  to  that,  for  they  are  both  radii  of  the  same  circle,  &c. 
There  is  certainly  a  mental  reference  in  such  cases  to  a 
Major  Premise,  —  to  the  well-known  truths,  that  No  cast- 
iron  is  malleable,  All  radii  of  the  same  circle  are  equal,  &c. 
But  precisely  because  such  Premises  are  well  known  and 
obvious,  though  thought,  they  are  not  usually  expressed. 

The  bald  truisms  which  are  usually  taken  as  examples 
of  the  Syllogistic  process  are  unfortunately  chosen,  as  they 
render  more  plausible  the  imputation  that  this  process  itself 
is  futile  and  needless.  Any  kind  of  reasoning  appears 
puerile,  when  it  is  applied  only  to  establish  a  puerile  Con- 
clusion. Nobody  wishes  any  proof  of  the  fact  that  Soc- 
rates was  mortal.  Adopt  any  supposition  which  will  make 
it  appear  that  there  was  a  real  doubt  in  the  case,  and  that 
the  point  to  be  determined  was  one  of  some  importance, 
and  the  Syllogism  employed  loses  its  frivolous  aspect,  and 
seems  grave  and  pertinent.  Suppose  that  the  impulsive 
Athenians  of  his  day  had  made  the  same  mistake  in  rela- 
tion to  Socrates,  that  those  of  a  later  time  committed  in 
regard  to  Paul  and  Barnabas,  and  had  begun  to  offer  sac- 
rifices to  him  as  an  immortal  being ;  it  would  have  been 


232  MEDIATE  INFERENCE   OR   SYLLOGISM. 

dignified  and  conclusive  on  his  part  to  argue  with  them,  as 
the  Apostle  did,  by  saying,  "  We  are  men  of  like  passions 
with  you,"  and  worship  is  due  only  unto  God.  The  first 
question  for  the  inquirer  or  disputant  is,  not  whether  this 
case  has  already  been  decided,  and  therefore  included 
under  this  General  Rule,  which  is  supposed  to  be  already 
found ;  but  under  what  Class-notion  can  this  case  be  put, 
which  shall  afford  a  General  Rule  that  will  be  applicable 
for  the  solution  of  the  doubt.  The  difficulty  is,  how  to 
find  the  right  Rule,  and  not,  as  Mr.  Mill  supposes,  how  to 
interpret  it  when  found.  The  astronomer  proceeds  in  this 
manner,  when  he  seeks  to  know  whether  a  comet,  which 
has  just  appeared  in  the  heavens,  will  return  at  a  future 
period,  or  disappear  forever.  By  determining  three  or 
more  points  in  its  path,  he  ascertains  either  that  its  orbit  is 
an  ellipse  or  an  hyperbola;  this  is  the  Subsumption,  and 
when  found,  the  question  is  really  answered,  for  the  appli- 
cation of  the  Sumption  —  that  the  ellipse  is  a  curve  which 
returns  into  itself,  while  the  hyperbola  does  not  —  is  so 
obvious,  that  it  is  unnecessary,  except  for  a  child,  to  be 
reminded  of  it.  But  though  not  expressed,  the  thought 
without  it  is  certainly  incomplete,  and  the  main  question  is 
not  answered. 

Mr.  Mill's  doctrine  is,  that  "  we  much  oftener  conclude 
from  particulars  to  particulars  directly,  than  through  the 
intermediate  agency  of  any  general  proposition."  For  ex- 
ample, "it  is  not  only  the  village  matron,  who,  when 
called  to  a  consultation  upon  the  case  of  a  neighbor's  child, 
pronounces  on  the  evil  and  its  remedy  simply  on  the  rec- 
ollection and  authority  of  what  she  accounts  the  similar 
case  of  her  Lucy." 

"We  have  already  observed  (page  9)  that  a  Concept  may 
be  derived  from  one  object,  as  well  as  from  many  similar 
ones  ;  that  is,  it  may  not  represent  an  actual,  but  only  a 
possible,  class  or  plurality  of  things.    The  hasty  and  sweep- 


THE  HAMILTONIAN  ANALYSIS.  233 

ing  inductions  of  the  vulgar  are  of  this  character  ;  they  are 
often  generalizations  from  a  single  instance.  The  medicine 
which  they  have  once  successfully  tried  is  believed  by  them 
to  be  a  panacea.  The  unhesitating  confidence  with  which 
the  village  matron  pronounces,  not  merely  on  one  case  of 
measles  or  whooping-cough  in  her  neighbor's  family,  but 
on  every  one  that  occurs  in  the  village,  proves  that  sbe 
has  generalized  her  Lucy's  case. 

All  general  truths  are  not  learned  by  induction  from 
particulars.  They  are  sometimes  first  obtained  by  Intu- 
ition, as  in  the  case  of  axioms  and  other  necessary  truths, 
or  by  reasoning  from  the  causes  or  conditions  on  which 
they  depend;  and  then,  individual  truths  are  proved  by 
deduction  from  these  generals.  Most  of  the  truths  of  pure 
mathematics  are  thus  acquired.  To  borrow  an  example 
from  Hobbes,  —  because  we  know  how  a  circle  is  gener- 
ated, namely,  by  the  circumduction  of  a  body  one  end  of 
which  is  fixed,  we  know  that  all  radii  of  the  same  circle 
are  equal.  Most  of  the  beautiful  applications  of  algebraic 
theorems  to  the  solution  of  arithmetical  and  geometrical 
problems  were  first  ascertained  to  be  possible  long  after  the 
general  theorems  themselves  were  discovered.  Such  meta- 
physical principles  as  these,  Every  event  must  have  a  cause, 
All  attributes  presuppose  a  substance,  Space  is  infinite  and 
indestructible,  were  not  first  made  known  to  us  by  induc- 
tion, and  cannot  be  proved  by  that  method.  Yet  the  ob- 
jection to  the  Syllogistic  process,  that  the  Major  Premise 
could  not  be  posited  if  the  truth  of  the  Conclusion  were 
not  already  known,  has  neither  force  nor  relevancy,  if  it 
be  not  proved  that  all  general  truths  are  obtained  by  in- 
duction, and  that  the  induction  was  so  perfect  that  it  must 
have  consciously  included  the  very  case  which  we  are  now 
seeking  to  deduce  from  the  general  rule. 

Hamilton's  next  innovation  in  the  theory  of  Logic  — 
and  it  is  one  which  was  propounded  by  him  at  an  eariiei 


234  MEDIATE  INFERENCE   OR   SYLLOGISM. 

day  than  his  doctrine  of  the  quantification  of  the  Predicate 
—  was  to  draw  attention  to  the  fact,  that  reasoning  does 
not  proceed,  as  had  formerly  been  taught,  solely  in  the 
Quantity  of  Extension,  but  also  in  the  Quantity  of  Inten- 
sion, the  relations  of  whole  and  part,  on  which  he  considers 
that  the  whole  process  depends,  being  reversed  in  these 
opposite  Quantities.  It  has  already  been  mentioned,  that, 
in  one  sense,  the  Predicate  of  every  Judgment  includes  the 
Subject,  and  therefore,  as  the  greater  or  more  Extensive 
Term,  it  was  called  the  Major,  and  the  Subject  was  desig- 
nated as  the  Minor  Term.  As  thus  construed,  the  Judg- 
ment, Man  is  an  animal,  means  that  the  class  Man  is  in- 
cluded under,  or  forms  a  part  of,  the  class  animal.  But  in 
another  sense,  —  that  is,  in  the  Quantity  of  Intension,  — 
the  Subject  includes  the  Predicate,  and  the  relations  of 
whole  and  part  are  reversed.  Interpreted  Intensively,  this 
Judgment  signifies  that  all  the  attributes  of  animal  are 
contained  in  or  among  —  form  a  part  of —  the  attributes  of 
man.  The  Subject  is  now  the  Major  Term,  and  the  Pred- 
icate is  the  Minor  ;  and  the  rule  being  still  adhered  to,  that 
the  Major  Premise  must  be  stated  first,  the  order  of  the 
Premises  is  reversed. 

Hamilton  gives  the  following  example  of  reasoning  in 
Extension. 

All  responsible  agents  are  free  agents ; 

But  man  is  a  responsible  agent ; 

Therefore,  man  is  a  free  agent. 
The  Premises  are  stated  in  this  order  on  the  supposition 
that  "free  agents,"  as  the  more  Extensive  class,  is  the 
whole  or  the  Major  Term,  that  "  man,"  having  the  least 
Extension,  is  the  smallest  part  or  the  Minor  Term,  and 
that  the  Middle  Term,  "responsible  agent,"  as  interme- 
diate between  the  two,  is  made  the  Subject  of  the  former, 
as  contained  under  it,  and  the  Predicate  of  the  latter,  which 
is  only  a  part  of  it.     In  other  words,  man  is  a  part  of  that 


THE  HAMILTONIAN  ANALYSIS.  235 

Tei  m  responsible  agent,  which  is  itself  a  part  of  the  Term 
free  agent ;  and  therefore,  as  a  part  of  a  part  is  a  part  of 
the  whole,  man  is  a  free  agent 
Now  reverse  the  Premises. 

Man  is  a  responsible  agent ; 

But  a  responsible  agent  is  a  free  agent ; 

Therefore,  man  is  a  free  agent. 
Here,  the  notion  free  agent,  which  was  the  greatest  whole, 
becomes  the  smallest  part ;  and  the  notion  man,  which  was 
the  smallest  part,  becomes  the  greatest  whole.  u  The 
notion  responsible  agent  remains  the  Middle  quantity  or 
notion  in  both,  but  its  relation  to  the  two  notions  is  re- 
versed ;  what  was  formerly  its  part  being  now  its  whole, 
and  what  was  formerly  its  whole  being  now  its  part." 

Hence,  in  the  First  Figure  (but  not,  as  we  shall  see,  in 
the  two  other  Figures),  the  order  in  which  the  two  Prem- 
ises are  placed  always  indicates  the  Quantity  in  which  we 
are  reasoning.  If  the  Major  Premise  contains  the  Subject 
of  the  Conclusion,  then  this  Subject  is  the  Major  Term,  and 
the  reasoning  is  in  Intension.  But  if  the  Predicate  of  the 
Conclusion  appears  in  the  first  Premise,  then  this  Predicate 
is  the  Major  quantity,  and  the  reasoning  is  in  Extension. 

But  as  this  indication  is  a  faint  one,  and  may  mislead  in 
the  case  of  the  Second  or  the  Third  Figure,  it  is  easy  to 
change  the  phraseology  of  the  Judgments,  so  as  to  enounce 
explicitly  whether  the  reasoning  concerns  the  Intensive, 
metaphysical,  whole  (the  Whole  of  the  Marks  connoted),  or 
the  Extensive,  logical,  whole  (the  whole  of  the  Individuals 
and  Species  denoted).    Thus,  for  the  latter,  we  may  say,  — 

All   responsible   agents  are  included  in  the  class  of  free 

agents ; 
But  man  is  a  responsible  agent ; 
Therefore,  man  is  included  in  the  class  of  free  agents. 

And  the  reasoning  of  Intension  mav  be  thus  stated :  — 


236  MEDIATE   INFERENCE   OR   SYLLOGISM. 

The  notion  or  Concept,  man,  includes  the  notion  of  respon- 
sibility ; 
But   the   notion   of  responsibility   includes    that    of  free 

agency ; 
Therefore,  the  notion,  man,  includes  the  notion  of  free- 
agency. 
It  is  the  more  remarkable  that  nearly  all  the  logicians 
since  Aristotle  should  have  contemplated  exclusively  rea- 
soning in  Extension,  as  Aristotle  himself  seems  to  have 
regarded  reasoning  in  Intension  as  coextensive  with  the 
former,  even  if  not  paramount  to  it.  Hamilton  has  only 
restored  the  doctrine  of  the  great  founder  of  Logic,  which 
had  been  strangely  overlooked  by  nearly  the  whole  tribe 
of  his  commentators  and  followers.  As  already  remarked, 
the  being  in  a  Subject  and  the  being  predicated  of  a  Sub- 
ject are  used  by  Aristotle  as  synonymous  phrases.  "  A 
is  predicated  of  all  B,"  means  All  B  is  A;  "A  is  in  (or 
inheres  in,  (map^eiv)  all  B"  also  means  All  B  is  A. 
The  meaning  evidently  is,  that,  in  the  Quantity  of  Inten- 
sion, the  Predicate  is  in  the  Subject  because  it  constitutes 
a  part,  and  only  a  part,  of  the  Intension  of  the  Subject. 
Animal  is  in  man,  because  man  has  all  the  attributes  or 
Marks  of  animal,  and  other  attributes  also. 

But  the  relation  of  whole  and  part  is  not  precisely  the 
same  thing  in  the  one  Quantity  as  in  the  other.  In  Exten- 
sion, the  whole  is  the  Genus,  and  the  parts  are  the  subor- 
dinate Species ;  and  the  first  Rule  for  the  division  is,  that 
the  parts,  or  the  co-ordinate  Species,  must  exclude  each 
other.  But  in  Intension,  the  parts  are  not  Species,  but 
attributes  or  Marks  ;  and  these  do  not  exclude  each  other. 
Each  part  or  attribute  here  interpenetrates,  so  to  speak, 
and  informs,  the  whole.  Black  is  a  part  of  negro  in  the 
sense  of  being  only  one  of  his  attributes,  since  he  has  many 
others,  such  as  being  long-heeled,  prognathous,  &c. ;  but  it 
is  a  part  which  colors  the  whole,  for  the  negro  is  black  all 


THE  HAMILTONIAN  ANALYSIS.  237 

over.  But  if  we  consider  the  Extension,  if  the  Genus  man 
is  subdivided  into  the  co-ordinate  Species  white  man  and 
black  man,  these  parts  exclude  each  other;  no  one  man 
can  belong  at  the  same  time  to  both  Species,  —  can  be  both 
white  and  black. 

Hence  the  maxim,  that  a  part  of  a  part  is  also  a  part  of 
the  whole,  is  not  a  universal  maxim  of  all  reasoning ;  as  it 
refers  only  to  co-exclusive  parts,  it  is  applicable  only  to 
reasoning  in  Extension.  The  corresponding  maxim  for 
reasoning  in  Intension  is,  that  a  Mark  of  a  Mark  is  also  a 
Mark  of  the  thing  itself  —  of  the  whole  thing ;  nota  notce 
est  nota  rei  ipsius.  Free  agency,  which  is  a  Mark  of 
responsibility,  is  also  a  Mark  of  man,  because  responsibility 
is  a  Mark  of  the  whole  man.  On  the  other  hand,  reason- 
ing Extensively,  we  say,  men  are  a  part  or  class  of  respon- 
sible agents,  and  are,  therefore,  also  a  part  of  free  agents, 
because  responsible  agents  are  a  part  of  free  agents. 

By  not  attending  to  this  distinction,  Hamilton  was  be- 
trayed on  one  occasion  into  propounding  as  a  valid  syllo- 
gism one,  which,  if  the  language  be  construed  literally,  is 
illogical ;  and  into  censuring  as  illogical  another,  which,  as 
stated,  is  certainly  irrecusable.  It  is  true  that  the  error 
consisted  entirely  in  the  use  of  language.  As  he  under- 
stood them,  his  approbation  of  the  one  and  his  censure  of 
the  other  are  correct ;  but  from  his  use  of  language,  no 
other  person  would  so  understand  them.  In  his  Lectures 
on  Logic,  while  illustrating  the  Special  Rule  of  an  Inten- 
sive Syllogism  (page  223,  Am.  ed.),  that  the  Sumption 
must«be  Affirmative,  and  the  Subsumption  Universal,  he 
states  the  following  as  a  valid  Syllogism  :  — 


S  comprehends  M  ; 

M  does  not  comprehend  P  ; 

Therefore  S  does  not  comprehend  P." 


238  MEDIATE  INFERENCE   OR   SYLLOGISM. 

If  the  language  be  interpreted  literally,  the  Conclusion 
here  is  illogical ;  for  it  is  evident,  from  the  diagram  which 
we  have  annexed,  that,  though  S  comprehends  M,  and  M 
excludes  P,  it  may  yet  be  true  that  S  comprehends  P. 

On  the  same  page,  he  censures  the  following  as  a  non 
sequitur^  though  the  diagram  here  annexed  demonstrates  it 
to  be  valid. 

S  does  not  compre- 
hend M ; 

But  M  comprehends  P  ; 

Therefore  S  does  not 
comprehend  P. 

But  instead  of  the  proposition  "  S  comprehends  M,"  sub- 
stitute the  meaning  which  was  intended,  that  S  has  M  for 
one  of  its  Marks  or  attributes,  and  make  the  corresponding 
change  throughout,  and  Hamilton's  verdict  upon  the  two 
Syllogisms  becomes  correct.  M,  though  only  one  of  the 
attributes  of  S,  affects  or  colors  the  whole  of  S ;  therefore, 
P,  which  is  not  an  attribute  of  M,  —  does  not  affect  any 
part  of  M,  —  is  not  an  attribute  of  S  ;  —  S  does  not  in- 
clude P  among  its  attributes.  The  Syllogism  which  is  ap- 
proved corresponds,  in  Form,  to  the  following,  which  is 
evidently  valid. 

A  negro  has  a  black  skin ; 

But  a  black  skin  is  not  an  invariable  sign  of  a  brute  in- 
tellect ; 
Therefore,  a  negro  is  not  necessarily  brutish  in  intellect. 

And  the  Syllogism  which  is  rejected  is  the  following :  — 
A  negro  is  not  white ; 
But  whites  are  civilized ; 
Therefore,  a  negro  is  not  civilized. 

In  fact,  the  mode  of  symbolizing  Syllogisms  by  circles,  as 


THE  HAMILTONIAN  ANALYSIS.  239 

well  as  the  maxim,  a  part  of  a  part  is  also  a  part  of  the 
whole,  is  inapplicable  to  the  Intensive  Syllogism ;  for  here 
the  "  parts  "  are  Marks  or  attributes  ;  and  these  are  not 
co-exclusive.     They  are  not  partes  extra  partes. 

It  is  with  some  reason,  then,  that  Mr.  DeMorgan  objects 
to  considering  the  Intension  of  a  Concept  as  a  quantity. 
In  the  vague  sense  of  being  susceptible  of  more  and  less,  it 
is  a  quantity  ;  but  so  far  as  it  is  incapable  of  exact  measure* 
ment,  it  is  not  a  quantity.  "  As  to  extent,"  he  says,  "  200 
instances  bear  a  definite  ratio  to  100,  which  we  can  use, 
because  our  instances  are  homogeneous.  But  different  quali- 
ties or  descriptions  can  never  be  numerically  summed  as 
attributes  to  any  purpose  arising  out  of  their  number. 
Does  the  idea  of  rational  animal,  two  descriptive  terms, 
suggest  any  useful  idea  of  duplication,  when  compared  writh 
that  of  animal  alone  ?  When  we  say  that  a  chair  and  a 
table  are  more  furniture  than  a  chair,  which  is  true,  we 
never  can  cumulate  them  to  any  purpose,  except  by  ex- 
tracting some  homogeneous  idea,  as  of  bulk,  price,  weight, 
&c.  To  give  equal  quantitative  weight  to  attributes,  as 
attributes,  seems  to  me  absurd ;  to  use  them  numerically 
otherwise,  is  at  present  impossible."  Perhaps  this  is  only 
saying  that  a  logician's  idea  of  quantity  is  not  the  same  as 
a  mathematician's ;  to  the  latter,  it  is  always  numerically 
definite,  or  may  be  made  so ;  to  the  former,  it  is  never  so. 
Perhaps,  if  Mr.  DeMorgan  had  kept  this  fact  steadily  in 
view,  a  good  many  of  his  attempted  innovations  in  Logic 
might  have  appeared,  even  to  him,  irrelevant. 

Hamilton  has  made  no  specific  innovation  in  the  doctrine 
of  the  Figures,  but  his  speculations  upon  the  subject  have 
thrown  a  flood  of  light  not  only  upon  the  essential  nature 
of  these  varieties  of  the  Syllogism,  but  upon  the  theories 
of  former  logicians  in  respect  to  them.  To  Aristotle,  on 
account  of  his  peculiar  method  of  stating  a  Judgment,  — ■ 
with  reference  to  the  Intension  instead  of  the  Extension  of 


240  MEDIATE  INFERENCE   OR   SYLLOGISM. 

its  Terms,  that  is,  placing  the  Predicate  first  and  the  Sub- 
ject last,  —  the  Middle  Term  was  intermediate  between 
the  two  others,  not  only  in  nature,  but  in  position.  Thus, 
the  following  are  only  two  different  expressions  of  the  same 
Syllogism. 

Aristotle's  form.  Later  or  common  form. 

P  inheres  in  (is  predicated  of)  all  M  ;     All  M  are  P  ; 
M  inheres  in  all  S  ;  All  S  are  M ; 

.-.  P  inheres  in  all  S.  .-.  All  S  are  P. 

Here,  in  Aristotle's  form,  P,  one  of  the  Extremes,  appears 
first,  and  S,  the  other  Extreme,  comes  last ;  M,  the  Middle 
Term,  in  both  of  its  expressions,  being  intermediate,  or 
coming  between  them.  In  the  later  form,  it  is  not  so. 
As  a  consequence  of  this  mode  of  statement,  in  his  defini- 
tion of  the  Second  Figure,  Aristotle  says  that  the  Middle 
Term  is,  by  its  position,  the  first ;  to  us,  on  the  contrary, 
it  is  the  last.  In  fact,  in  his  reduction  of  the  Second  and 
Third  Figures  to  the  First,  Aristotle  seems  to  have  had  in 
view,  not  only  the  establishment  of  the  dictum  de  omni  et 
nidlo  as  the  universal  principle  of  all  Syllogistic  reasoning, 
but  the  restoration  of  the  Middle  Term  to  its  proper  in- 
termediate position.  He  was  evidently  thinking  most  of 
reasoning  in  Intension,  and  his  followers  of  what  is  more 
frequent  in  use,  though  not  more  natural,  —  reasoning  in 
Extension.  In  the  later  form,  if  the  Minor  Premise  is 
stated  first,  the  Middle  Term  becomes  intermediate  in 
position,  as  in  the  Aristotelic  formula. 

In  this  exposition  of  Aristotle's  mode  of  enouncement, 
as  contrasted  with  that  of  the  later  logicians,  Hamilton  has 
merely  followed  Barthelemy  St.  Hilaire  ;  in  what  follows, 
he  is  more  original. 

"  When  logicians,"  he  says,  "  came  to  enounce  propo- 
sitions and  Syllogisms  in  common  language,  the  Subject 
being  usually  first,  they  had  one  or  other  of  two  difficulties 


THE  HAMILTONIAN  ANALYSIS.  241 

to  encounter,  and  submit  they  must  to  either ;  for  they 
must  either  displace  the  Middle  Term  from  its  interme- 
diate position  in  the  First  Figure,  to  say  nothing  of  revers- 
ing its  order  in  the  Second  and  Third ;  or,  if  they  kept  it 
in  an  intermediate  position  in  the  First  Figure  (in  the. 
Second  and  Third,  the  Aristotelic  order  could  not  be  kept), 
it  behooved  them  to  enounce  the  Minor  Premise  first." 
Most  of  the  older  logicians  adopted  the  latter  alternative, 
stating  the  Minor  Premise  first  in  all  the  Figures;  and 
this  seems  the  more  natural  order,  if  the  Syllogism  is  used 
for  the  purpose  of  investigation  and  discovery.  At  a  later 
period,  when  instruction,  disputation,  and  proof  came  to 
be  the  chief  purposes  for  which  Syllogisms  were  formally 
enounced,  the  former  alternative  was  adopted,  and  the 
Middle  Term  lost  its  proper  intermediate  position,  the 
Major  Premise  being  placed  first  in  all  the  Figures. 

In  the  First  Figure,  according  to  any  mode  of  enounce- 
ment,  the  Middle  Term  must  be  the  Subject  of  one  of  the 
Extremes  (the  two  Terms  of  the  Conclusion),  and  the 
Predicate  of  the  other.  Hence,  in  this  Figure,  there  is  a 
determinate  Major  and  Minor  Premise  for  reasoning  in 
either  Quantity,  and  but  one  direct  or  proximate  Conclu- 
sion. If,  in  the  Major  Premise,  the  Middle  Term  is  Predi- 
cate to  the  Subject  of  the  Conclusion,  then,  in  each  of  the 
three  Judgments,  the  Subject  includes  the  Predicate,  and  the 
reasoning  is  in  the  Quantity  of  Intension.  If,  on  the  con- 
trary, in  the  Major  Premise,  the  Middle  Term  is  Subject  to 
the  Predicate  of  the  Conclusion,  then,  in  each  of  the  three 
Judgments,  the  Predicate  includes  the  Subject,  and  the  reason- 
ing is  in  the  Quantity  of  Extension.  The  relative  position 
of  the  two  Premises  is  really  unimportant  as  respects  the 
nature  of  the  reasoning ;  this  depends  upon  the  nature  of 
the  Middle  Term,  as  including,  or  included  under,  the  Sub- 
ject of  the  Conclusion.  But  following  the  established 
order  of  logical  Quantity,  that  the  greater  should  be  placed 
u  p 


242  MEDIATE  INFERENCE   OR  SYLLOGISM. 

first,  the  Middle  Term  as  Subject,  and  the  Predicate  of 
the  Conclusion  as  Predicate,  should  be  the  first  or  Majoi 
Premise  for  reasoning  in  Extension ;  and  the  Middle  Term 
as  Predicate,  with  the  Subject  of  the  Conclusion  as  Sub- 
ject, should  be  the  first  or  Major  Premise  in  Intension 
Thus :  — 

In  Extension,  In  Intension. 

M  is  P  ;  S  is  M  ; 

S  is  M  ;  M  is  P  ; 

.*.  S  is  [included  under]  P.         .*.  S  is  [includes]  P. 

Here,  the  relation  of  the  Terms  to  each  other  in  the 
Premises  determines  their  relation  to  each  other  in  the  Con- 
clusion. If,  in  the  Premises,  M  is  included  under  P,  and 
S  included  under  M,  then,  in  the  Conclusion,  S  must  be 
included  under  P.  But  if,  in  the  Premises,  S  includes  M, 
and  M  includes  P,  then,  in  the  Conclusion,  S  must  include 
P.  Hence,  in  the  First  Figure,  there  can  be  but  one 
direct  Conclusion. 

In  the  two  other  Figures,  it  is  not  so.  The  Middle 
Term  is  not  Subject  of  one  and  Predicate  of  the  other  Ex- 
treme, but  is  either,  as  in  the  Second  Figure,  Predicate  of 
both,  or,  as  in  the  Third,  Subject  of  both.  Consequently, 
in  each  of  these  Figures,  the  Middle  Term  either  includes 
both  the  Extremes,  or  is  included  under  both.  As  there 
is  nothing,  then,  to  determine  the  relative  Quantity  of  the 
two  Extremes  to  each  other,  either  may  be  considered  as 
Major  in  the  Conclusion ;  —  we  may  conclude  either  that 
S  is  P,  or  that  P  is  S. 

Though  the  First  Figure  has  but  one  direct  or  immediate 
Conclusion,  we  may,  by  the  medium  of  Conversion,  obtain 
from  it  another  Conclusion,  which  is  then  properly  called 
indirect  or  mediate.  Thus*  in  the  formulas  just  given,  hav- 
ing concluded  directly  that  All  S  is  P,  we  may  then  con- 
clude indirectlv,  or  mediately,  that  Some  P  is  S.     But  in 


THE  HAMILT0N1AN  ANALYSIS.  243 

the  other  Figures,  there  are  two  indifferent  Conclusions, 
neither  of  which  is  more  direct  or  immediate  than  the 
others.  If  A  is  B  and  C  is  B,  we  may  conclude,  with 
equal  propriety  and  directness,  either  that  A  is  C,  or 
C  is  A;  for  there  is  nothing  in  the  Premises  to  indicate 
whether  A  includes,  or  is  included  under,  C.  And  in  like 
manner  in  the  Third  Figure ;  if  B  is  A  and  B  is  C,  the 
two  Conclusions,  A  is  C  and  C  is  A,  are  equally  compe- 
tent and  equally  immediate.  Of  course,  what  has  been 
called  the  Fourth  Figure  is  merely  the  First,  with  its  indi- 
rect Conclusion  enounced  as  if  it  were  direct  or  imme- 
diate ;  it  is  a  hybrid  reasoning,  with  its  two  Premises  in 
one  Quantity,  and  its  Conclusion  in  the  other.  Hence 
the  Fourth  Figure  is  properly  abolished. 

In  fact,  all  difference  of  Figure  is  unessential,  —  a  mere 
accident  of  form.  As  it  is  demonstrated  in  the  Hamil- 
tonian  analysis,  that  a  Judgment  is  a  mere  equation  of  its 
two  Terms,  it  makes  no  difference  which  is  stated  first,  — 
which  is  Subject  or  which  is  Predicate  ;  A  =  B  and  B  =  A 
are  the  same  equation.  Quantify  the  Predicate  through- 
out, and  this  becomes  evident.  As  all  Conversion  is  then 
reduced  to  Simple  Conversion,  we  have  only  to  convert 
simply  (retaining  the  subordination  of  the  Terms)  the 
Major  Premise  of  the  First  Figure  in  Extension,  in  order 
to  produce  the  Second  Figure  ;  convert  its  Minor  Premise, 
and  we  have  the  Third.  In  Intension,  this  is  merely  re- 
versed ;  convert  the  Minor  for  the  Second,  and  the  Major 
for  the  Third. 

To  make  the  Syllogistic  process  depend  upon  the  mere 
position,  either  of  the  two  Terms  as  Subject  or  Predicate, 
or  of  the  two  Premises  as  enounced  first  or  second,  or  of 
the  Conclusion  as  expressed  first  or  last,  is  to  reduce  Rea- 
soning to  a  mere  accident  of  expression,  and  cause  it  to 
vary  with  the  genius  of  different  languages,  or  even  with 
the  mental   peculiarities  of  individuals.      Reasoning  is  a 


244  MEDIATE   INFERENCE   OR   SYLLOGISM. 

process  of  Thought,  not  of  language.  It  depends  solely 
upon  the  relations  of  inclusion  and  exclusion,  of  subor- 
dination and  superordination,  of  Intension  and  Exten- 
sion, existing  between  two  Concepts  and  a  Third ;  and  it 
must  be  regulated  by  universal  laws,  irrespective  of  differ- 
ences of  language  and  peculiarities  of  mental  habit.  The 
order  of  enouncement  is  a  convenient,  though  conven- 
tional,  mode  of  indicating  these  relations  to  other  persons, 
and  even  a  safeguard  against  confusion  and  error  in  the 
successive  elaboration  of  them  in  our  own  minds.  But  the 
actual  inference,  the  mental  process  as  such,  is  entirely 
independent  of  this  order. 

To  show  further  the  unessential  character  of  variation  by 
Figure,  Hamilton  pointed  out  the  manner  of  abolishing  the 
distinction  of  Subject  and  Predicate,  and  thereby  reducing 
all  Mediate  Inference  to  what  he  calls  the  Unfigured  Syl- 
logism. Any  Syllogisms  whatever  may  find  adequate, 
though  awkward,  expression  under  this  form.  The  two  fol- 
lowing instances  will  suffice. 

Fig.  I.  Darii,        reduced  to  an         Unfigured  Syllogism. 

All  patriots  are  brave ;  All  patriots  and  some  brave  men 

are  equal ; 
Some  persecuted  men  are         Some  persecuted  and  some  pa- 
patriots  ;  triots  are  equal ; 
.*.  Some  persecuted  men  are     .*.  Some  persecuted  and  some  brave 
brave.                                       men  are  equal. 

Fig.  II.  Camestres. 

All  animals  are  sentient  ;  All  animals  and   some  sentient 

v  things  are  equal ; 

Nothing    unorganized    is  Any  unorganized  and  any  sen- 

sentient ;  tient  are  not  equal ; 

..Nothing    unorganized    is  .'.Any  unorganized  and  any  an- 

animal.  imal  are  not  equal. 

In  this  Unfigured  Syllogism,  as  Hamilton  remarks,  "  the 


THE  HAMILTONIAN  ANALYSIS.  245 

dependency  of  Extension  and  Intension  does  not  subsist, 
and  accordingly  thj  order  of  the  Premises  is  wholly  arbi- 
trary. This  form  has  been  overlooked  by  the  logicians, 
though  equally  worthy  of  development  as  any  other ;  in 
fact,  it  affords  a  key  to  the  whole  mystery  of  Syllogism. 
And  what  is  curious,  the  Canon  by  which  this  Syllogism  is 
regulated  (what  may  be  called  that  of  logical  Analogy  or 
Proportion)  has,  for  above  five  centuries,  been  commonly 
stated  as  the  one  principle  of  reasoning,  whilst  the  form  of 
reasoning  itself,  to  which  it  properly  applies,  has  never  been 
generalized.  This  Canon,  which  has  been  often  errone- 
ously, and  never  adequately  enounced,  in  rules  four,  three, 
two,  or  one,  is  as  follows :  —  In  as  far  as  two  notions 
(notions  proper  or  individuals^)  either  both  agree,  or  one 
agreeing  the  other  does  not,  with  a  common  third  notion ;  in 
so  far  these  notions  do  or  do  not  agree  with  each  other.  This 
Canon  thus  excludes,  —  1.  an  undistributed  Middle  Term, 
as  then  no  common  notion ;  —  2.  two  negative  Premises, 
as  then  no  agreement  of  either  of  the  other  notions  there- 
with.'' 

A  convenient,  though  somewhat  mechanical,  rule  for 
drawing  the  correct  Conclusion  from  any  pair  of  Premises 
is  the  following,  which  was  first  stated  by  Ploucquet,  and 
after  him  by  Mr.  De  Morgan.  Erase  the  symbols  of  the 
Middle  Term,  the  remaining  symbols  show  the  inference. 
Deleatur  in  pr&missis  medius  ;  id  quod  restat  indicat  conclu- 
sionem.  Thus,  in  the  two  Syllogisms  just  given  and  re- 
duced to  the  Unfigured  form,  strike  out  from  the  Prem- 
ises, what  I  have  italicized,  all  that  relates  to  the  Middle 
Term,  and  what  remains  of  the  Premises  is  the  Conclu- 
sion. But  it  should  be  mentioned  that  this  Rule,  though 
valid  for  all  the  Aristotelic  moods,  does  not  hold  good,  as 
we  shall  see,  for  all  the  moods  recognized  under  the  Ham- 
iltonian  system. 

Perhaps  the  most  striking,  and  certainly  the  most  con- 


246  MEDIATE   INFERENCE   OR  SYLLOGISM. 

venient,  improvement  which  Sir  William  Hamilton  has 
made  upon  the  labors  of  former  logicians,  is  his  system  of 
notation,  —  a  masterpiece  of  ingenuity  in  symbolization  as 
respects  perspicuity,  completeness,  and  simplicity.  It  is 
valid  for  any  system,  and  it  manifests,  at  once,  nearly  all 
the  alterations  and  improvements  which  he  has  made  in 
the  Aristotelic  doctrine.  It  shows  at  a  glance  the  equiv- 
alent Syllogisms  in  the  different  Figures,  the  convertible 
Syllogisms  in  the  same  Figure,  and  points  out  the  two 
meanings  which  can  be  given  to  every  Syllogism  as  inter- 
preted according  to  its  Extension  or  its  Intension,  in  refer- 
ence to  the  logical  or  the  metaphysical  whole.  Even  as  a 
mnemonic  contrivance,  it  is  second  in  ingenuity  and  useful- 
ness only  to  the  famous  quatrain  of  hexameters,  which 
contains  the  whole  doctrine  of  the  Reduction  of  the  Moods 
of  the  lower  Figures  to  the  first  Figure. 

The  purpose  of  any  system  of  notation  is  to  manifest,  by 
the  differences  and  relations  of  geometrical  quantities  (lines 
or  figures),  the  differences  and  relations  of  logical  forms. 

A  Proposition  or  Judgment  is  here  indicated  by  a  straight 
horizontal  line,  its  two  Terms  or  Extremes  being  placed  at 
the  extremities  of  that  line,  and  represented,  as  usual,  by 
letters. 

If,  as  in  the  Unfigured  Syllogism,  there  is  no  distinction 
of  Subject  and  Predicate,  this  line  is  made  of  equal  thick- 
ness throughout.  But  if  this  distinction  is  introduced, 
then,  as  it  is  possible  to  read  the  Judgment  in  two  ways, 
according  to  the  Extension  or  the  Intension  of  its  Terms, 
(the  Subject,  in  the  latter  case,  including  the  Predicate, 
and  in  the  former,  being  included  under  it,)  the  line  is 
made  wedge-shaped.  Its  broad  end  then  represents  the 
Subject  of  Extension  or  Breadth,  and  the  thin  end,  that  of 
Intension  or  Depth.  A  line  gradually  diminishing  or  in- 
creasing from  end  to  end  aptly  indicates  the  relation  be- 
tween two  Quantities  which  are  always  co-existent,  and  in 


THE  HAMILTONIAN  ANALYSIS.  247 

inverse  ratio  to  each  other.  As  the  employment  of  letters 
following  upon  each  other  in  the  same  alphabet  might  sug- 
gest that  one  was  invariably  subordinated  to  the  other, 
instead  of  being  its  subordinate  in  one  Quantity  and  its 
superordinate  in  the  other,  Hamilton  uses  for  the  Extremes 
the  Latin  C  and  Greek  T,  each  being  the  third  letter  in 
its  own  alphabet ;  as  usual,  M  stands  for  the  Middle  Term. 
Thus:  — 

is  read,  O  and  T  are  equal. 

c  — r 

may  be  read  in  two  ways;  Extensively,  O  is  included 
under  T;  Intensively,  F  is  included  in  C:  —  or,  in  the 
usual  manner,  0  is  T,  and  T  is  C,  merely  remembering, 
without  saying  so,  that  Extension  is  signified  in  the  former 
case,  and  Intension  in  the  latter. 

Negation  is  indicated  by  a  perpendicular  stroke  drawn 
through  the  line,  thus :  ^H — •  The  line  without  this  stroke 
may  be  regarded  as  the  Affirmative  Copula;  with  the 
stroke,  as  the  Negative  Copula.  A  colon  (:)  annexed  to  a 
Term  shows  that  it  is  distributed,  or  taken  universally  ;  a 
comma  (,)  so  annexed,  that  it  is  undistributed  or  Particu- 
lar. When  a  Middle  Term  has  a  colon  on  the  right,  and  a 
comma  on  the  left,  it  is  understood  that  it  is  distributed 
when  coupled  in  a  Judgment  with  the  Term  on  the  right, 
and  undistributed  when  coupled  with  the  other. 

A  line  drawn  beneath  or  above  three  Terms  indicates 
the  Conclusion  (or  the  Copula  of  the  Conclusion)  deduced 
from  the  two  Premises  which  those  Terms  constitute.  In 
the  Second  and  Third  Figures,  since  there  may  be  two 
equally  direct  or  immediate  Conclusions,  they  are  repre- 
sented by  two  such  lines,  the  one  above,  and  the  other 
below  the  Premises.     Thus  :  — 

iw  in  This  is  a  Syllogism  in  the  Second 

C,  ■         ,  M  :  — -^ ,  r     Figure,  which  may  be   read   in 
^■mm  either  of  the  following  ways. 


248  MEDIATE  INFERENCE   OR  SYLLOGISM. 

Extensively.  Intensively. 

Some  C  is  some  M ;  All  M  is  some  T  ; 

Some  r  is  all  M  ;  Some  M  is  some  C  ; 

/.  Some  r  is  some  C ;  or  .-.  Some  C  is  some  T  ;  or 

.*.  Some  C  is  some  T.  .*.  Some  T  is  some  C. 

q  ,   Tyr .      I    m  .  p      This  is  a  Negative  Syllogism  in 

,  the   First  Figure,  which  may  be 

read  in  either  of  the  following 
ways ;  but  in  either  way,  it  has  only  one  direct  or  imme- 
diate Conclusion,  though  a  Second  Conclusion  may  be  ob- 
tained from  it  indirectly,  by  converting  simply  the  proper 
or  direct  Conclusion. 

Extensively.  Intensively. 

Some  M  is  some  C  ;  No  M  is  any  T  ; 

No  r  is  any  M  ;  Some  C  is  some  M  ; 

No  r  is  some  C ;  or,  Some   C  is  not  any  T  ;  or, 

indirectly,  indirectly, 

Some  C  is  not  any  T.  Not  any  T  is  some  C. 

The  following  diagram  presents  the  whole  Hamiltonian 
doctrine  of  Figure,  together  with  the  distinction  between 
the  Analytic  and  the  Synthetic  order  of  enouncement. 
After  the  explanations  which  have  been  given,  it  will  be 
easily  understood. 

As  a  Judgment  has  been  designated  by  a  line,  a  Syllo- 
gism, which  is  a  union  of  three  Judgments,  is  appropriately 
typified  by  a  triangle,  a  union  of  three  lines,  of  which  the 
base  represents  the  Conclusion,  and  the  other  two  lines, 
the  Premises.  As  the  direction  of  the  arrows  indicates, 
we  may  proceed  either  in  the  usual  or  Synthetic  order, 
from  the  Premises  to  the  Conclusion,  or  in  the  reverse 
order,  which  is  Analytic,  from  the  Conclusion  to  the  Prem- 
ises. As  there  is  no  valid  reason  for  always,  placing  the 
Major  Premise  first  in  order,  the  diagram  shows  that  either 
Premise  may  have  precedence  in  this  respect,  so  that  what 
has  been  called  the  Fourth  Figure  is  here  identified  with 
the  Indirect  Moods  of  the  First. 


THE  HAMILTONIAN  ANALYSIS.  249 

SIT 


>K      3K      $K 


The  Unfigured  Syllogism  is  properly  represented  as  in- 
cluding all  the  others,  as  any  Syllogism  of  either  Figure 
may  be  easily  expressed  in  this  form.  In  like  manner,  the 
triangle  representing  the  First  Figure  is  made  to  include 
the  two  typifying  respectively  the  Second  and  Third,  as 
either  of  the  latter  may  be  readily  reduced  to  the  former. 
And  again,  the  essential  unity  of  the  Syllogistic  process, 
and  the  unessential  nature  of  variation  by  Figure,  are  ap- 
propriately signified  by  a  single  triangle  comprehending  all 
the  varieties  of  form. 

"  The  double  Conclusions,  both  equally  direct,  in  the 
Second  and  Third  Figures,  are  shown  in  the  crossing  of 
two  counter  and  corresponding  lines.  The  Direct  and 
Indirect  Conclusions  in  the  First  Figure  are  distinctly 
typified  by  a  common  and  by  a  broken  line ;  the  broken 
line  is  placed  immediately  under  the  other,  and  may  thus 
indicate  that  it  represents  .mly  a  reflex  of —  a  consequence 
11* 


250  MEDIATE  INFERENCE   OR   SYLLOGISM. 

through — the  other  (tear  dvaKXaaiv,  reflexim,  per  re- 
flexioneni).  The  diagram  therefore  can  show,  that  the 
Indirect  Moods  of  the  First  Figure,  as  well  as  all  the  Moods 
of  the  Fourth,  ought  to  be  reduced  to  merely  mediate  in- 
ferences ;  —  that  is,  to  Conclusions  from  Conclusions  of  the 
conjugations  or  Premises  of  the  First  Figure." 

If  we  have  the  two  Premises,  All  C  is  some  M,  and  All 
31 is  some  J7,  and  consider  that  some  M  is  a  Mark  of  (or, 
is  included  in)  all  (7,  and  some  F  a  Mark  of  all  M,  then 
we  are  reasoning  in  the  Quantity  of  Intension ;  and,  accord- 
ing to  the  Axiom  that  a  Mark  of  a  Mark  is  also  a  Mark  of 
the  thing  itself  the  proper  and  direct  Conclusion  is,  All  C  is 
some  F.  But  if  we  conclude  that  Some  F  is  all  C,  accord- 
ing  to  the  Fourth  Figure  or  the  Indirect  Moods  of  the 
First,  Some  F  does  not  appear  as  a  Mark  of  all  C,  but  as 
included  under  it,  —  as  a  Subject  of  Extension  ;  the  Prem- 
ises, then,  would  be  represented  in  one  Quantity,  and  the 
Conclusion  in  the  other.  "  But  though  always  coexistent, 
and  consequently  always,  to  some  amount,  potentially  in- 
ferring each  other,  still  we  cannot,  without  the  interven- 
tion of  an  actual  inference,  at  once  jump  from  the  one 
Quantity  to  the  other,  —  change,  per  saltum,  Predicate 
into  Subject  and  Subject  into  Predicate.  We  must  pro- 
ceed gradatim.  We  cannot  arbitrarily  commute  the 
Quantities,  in  passing  from  the  Quassitum  to  the  Prem- 
ises, or  in  our  transition  from  the  Premises  to  the  Con- 
clusion. When  this  is  apparently  done,  the  procedure  is 
not  only  unnatural,  but  virtually  complex  and  mediate, 
the  mediacy  being  concealed  by  the  concealment  of  the  mental 
inference  which  really  precedes  "  ;  —  indicated  by  the  broken 
line  in  the  diagram. 

One  other  species  of  Hamiltonian  notation  should  be 
noticed,  as  it  brings  to  light  very  clearly  the  virtual  equiva- 
lence of  those  Moods  in  the  several  Figures  which  are  in- 
dicated, in  the  old  mnemonic  hexameters,  by  names  begin- 


THE  HAMILT0N1AN  ANALYSIS.  251 

ning  wich^the  same  capital  letter.  Four  straight  lines  are 
all  that  is  needed  for  such  a  notation.  Three  of  these  are 
horizontal,  to  represent  the  Terms  ;  and  one  perpendicular, 
or  the  want  of  it,  at  the  beginning  of  the  comparison,  to 
express  the  Quality  of  Affirmation  or  Negation.  "  Quan- 
tity is  marked  by  the  relative  length  of  a  terminal  line 
within,  or  its  indefinite  excursion  before,  the  limit  of  com- 
parison. This  notation  can  represent  equally  total  and 
ultratotal  distribution,  in  simple  Syllogism  and  in  Sorites ; 
and  it  shows  at  a  glance  the  competence  or  incompetence 
of  any  Conclusion." 


"  Of  these,  the  former,  with  its  converse,  includes  Darii, 
Dabitis,  Datisi,  Disamis,  Dimaris,  &c.  ;  whilst  the  latter, 
with  its  converse,  includes  Celarent,  Cesare,  Celanes,  Ca- 
mestres,  Cameles,  &c.  But  of  these,  those  which  are  rep- 
resented by  the  same  diagram  are,  though  in  different 
Figures,  formally  the  same  Mood."  "  In  all  the  other 
geometrical  schemes  hitherto  proposed,  whether  by  lines, 
angles,  triangles,  squares,  or  circles,  the  same  complex 
diagram  is  necessarily  employed  to  represent  an  indefinite 
plurality  of  Moods." 

The  application  of  Hamilton's  doctrine  of  the  thorough- 
going quantification  of  the  Predicate  to  the  explication  of 
the  Syllogistic  theory  produces,  as  might  have  been  ex- 
pected, a  great  enlargement  of  the  number  of  Moods.  If 
there  are  but  four  fundamental  Judgments,  the  number  of 
conceivable  Moods  that  can  be  framed  from  them,  by  taking 
them  three  and  three,  is  sixty-four  * ;  excluding  from  these 

*  The  computation  is  easily  made.     The  four  letters  A,  E,  I,  O,  give 
us  four  different  Major  Premises  ;  each  of  these  may  have  four  different 
Minor  Premises  ;  —  hence  there  will  he  sixteen   pairs  of  Premises.     But 
each  of  these  pairs  may  be  conceived  to  have  four  different  Conclusions 
whence,  1 6  X  4  =  64  conceivable  Moods. 


252  MEDIATE   INFERENCE   OR   SYLLOGISM. 

the  invalid  Moods,  as  offending  against  one  or  more  of 
the  general  Rules  of  the  Syllogistic  process,  there  remain 
only  fourteen  as  valid  in  some  one  of  the  first  three  Fig- 
ures ;  —  nineteen,  if  we  admit  the  Fourth  Figure  ;  —  twenty- 
four,  if  we  include  also  the  anonymous  indirect  Moods. 
But  under  the  Hamiltonian  doctrine  of  eight  fundamental 
Judgments,  we  have  five  hundred  and  twelve  *  conceivablo 
Moods.  Excluding  from  these  all  that  offend  against  the 
General  Canon,  (as  by  having  an  undistributed  Middle, 
two  Negative  Premises,  or  collecting  more  in  the  Conclu- 
sion than  was  distributed  in  the  Premises,)  there  remain 
thirty-six  valid  Moods,  of  which  twelve  are  Affirmative  and 
twenty-four  Negative.  On  this  doctrine,  each  Affirmative 
Mood  yields  two  Negative  ones,  as  each  of  its  Premises 
may  be  successively  negatived.  Figure  now  appears  in  its 
true  character,  as  an  unessential  variation ;  but  as  each  of 
these  valid  Moods  can,  if  we  please,  be  thrown  into  either 
of  the  three  Figures,  there  are  36  X  3  =  108  valid  Moods, 
reckoning  as  such  all  the  modifications  of  statement  of 
which  they  are  susceptible.  But  to  show  how  trifling  are 
the  changes  thus  effected  by  carrying  what  is  really  one 
Mood  through  each  of  the  three  Figures,  I  borrow  a  con- 
crete example  from  Mr.  Baynes. 

Fig.  I.  Fig.  II. 

All  man  is  some  animal ;  Some  animal  is  all  man  ; 

Every  Celt  is  some  man ;  Every  Celt  is  some  man ; 

•\  Every  Celt  is  some  animal.        .*.  Every  Celt  is  some  animal. 

Fig.  in. 

All  man  is  some  animal ; 

Some  man  is  every  Celt ; 

.*.  Every  Celt  is  some  animal. 

*  Computing  as  before,  from  eight  Judgments  we  have  eight  different 
Major  Premises,  each  of  which  may  have  eight  different  Minor  Premises, 
whence  8  X  8  =  64  pairs  of  Premises ;  and  as  each  of  these  may  have 
eight  different  Conclusions,  there  are  64  X  8  =  512  triplets  of  Judgments, 
or  conceivable  Syllogisms. 


THE  HAMILTONIAN  ANALYSIS.  253 

Hamilton's  General  Canon  has  already  been  enounced 
in  the  mode  of  statement  in  which  it  is  directly  applicable 
to  the  Unfigured  Syllogism.  As  applied  to  the  Figured 
Syllogism,  wherein  we  have  to  consider  the  two  counter 
Quantities  of  Extension  and  Intension,  it  should  be  thus 
expressed:  —  "  What  worse  relation  of  Subject  and  Predi- 
cate subsists  between  either  of  two  Terms  and  a  common 
Third  Term,  with  which  one  at  least  is  positively  [affirma- 
tively] related,  that  relation  subsists  between  the  two 
Terms  themselves."  As  already  stated,  this  Canon  is 
only  a  succinct  statement  of  the  six  general  Rules  which 
have  been  laid  down  as  fulfilled  in  every  valid  case  of 
Mediate  Inference  ;  and  it  is,  also,  only  a  restatement  of 
the  two  Primary  Axioms  of  Pure  Thought,  the  laws  of 
Identity  and  Non-Contradiction,  with  the  necessary  con- 
ditions and  limitations  which  determine  their  application. 
As  these  Rules  and  Axioms  were  found  to  hold  good  under 
the  Aristotelic  doctrine  of  four  fundamental  Judgments, 
they  are  also  valid  under  the  system  which  increases  the 
number  of  these  Judgments  to  eight.  No  Syllogism  can 
be  fn valid  which  accords  throughout  with  this  Canon,  and 
every  illegitimate  process,  either  directly  or  indirectly, 
openly  or  covertly,  violates  it. 

But  we  must  accurately  determine  which  is  the  "  worse 
relation  "  of  Subject  and  Predicate  that  can  subsist  be- 
tween either  of  two  Terms  and  a  common  Third  Term. 
When  there  are  but  four  Judgments,  the  corresponding 
principle,  that  the  Conclusion  follows  the  "  weaker  part," 
admits  of  easy  interpretation ;  Particular  Quantity  is 
weaker  than  Universal,  Negative  Quality  is  weaker  than 
Affirmation.  But  with  eight  Judgments,  the  various  de- 
grees of  better  or  worse,  stronger  or  weaker,  must  be 
more  precisely  ascertained.  Always  considering  Negation 
as  weaker  than  Affirmation,  we  now  say  that  the  best 
(strongest)  Quantity  of  Affirmation  is  the  ivorst  (weakest) 


254  MEDIATE   INFERENCE   OR   SYLLOGISM. 

Quantity  of  Negation.  In  other  words,  we  affirm  best  when 
we  affirm  all,  and  affirm  worst  when  we  affirm  only  some  ;  on 
the  contrary,  we  deny  best  when  we  deny  only  some,  and 
deny  worst  when  we  deny  all.  On  account  of  this  inverse 
relation  of  the  two  Quantities,  an  Affirmative  Mood  with  a 
Particular  Conclusion  may  be  changed,  by  merely  nega- 
tiving one  of  its  Premises,  into  a  Negative  Mood  with  a 
Universal  Conclusion.  But  though  the  Quantity  is  thus 
altered  from  Particular  to  Universal,  this  is  not  a  change 
from  worse  to  better,  but  from  worst  to  worst ;  for  though 
a  Particular  stands  lowest  in  the  scale  of  Affirmation,  a 
Universal  stands  lowest  in  the  scale  of  Negation.  The 
6eeming  exception  only  confirms  the  rule,  and  proves  that 
the  Canon  is  universally  applicable.  Take  the  following 
instance  :  — 

C  :  — -,  M  : —  :  V  Some  M  is  all  C  ; 

■  ,  All  T  is  all  M ; 

.-.  Some  T  is  all  C. 
Some  blacks  are  all  slaves ; 
All  of  African  descent  are  all  blacks  ; 
.*.  Some  of  African  descent  are  all  slaves. 

Now,  if  we  negative  this  Syllogism  by  negativing  the 
Minor  Premise,  the  Conclusion  changes  from  Particular  to 
Universal,  thus :  — 

n  _   A  r        ,     _    t.    Some  M  is  all  C  : 

,  No  r  is  any  M ; 

No  T  is  any  C. 

Some  blacks  are  all  slaves ; 
No  Caucasian  is  any  black ; 
.*.  No  Caucasian  is  any  slave. 

This  change,  though  from  Particular  to  Universal,  is 
really  from  the  worst  of  Affirmation  to  the  worst  of  Nega- 
tion.    But  such  changes  are  infrequent,  as,  in  the  inter- 


THE  HAMILTONIAN  ANALYSIS.  255 

mediate  relations,  the  commutation  is  only  from  equal  to 
equal,  and  the  predesignations  of  Quantity,  in  their  in- 
verse signification,  remain  externally  the  same.  Out  of 
the  twenty-four  valid  Negative  Moods,  only  four  cases  are 
found  of  a  Particular  quantification  disappearing  in  the 
Negative  Conclusion.  Hamilton  gives  the  following  ar- 
rangement of  the  eight  Judgments  in  the  order  proceeding 
from  best  to  worst. 

Best.       s—    1.  Afa.  All  are  all. 

—2.  Afi.  All  are  some. 

r — 3.  Ifa.  Some  are  all. 

/— 4.  Ifi.  Some  are  some. 

^-5.  Ini.  Some  are  not  some. 

— 6.  Ina.  Some  are  not  any. 

— 7.  Ani.  Not  any  is  some. 

— 8.  Ana.  Not  any  is  any. 


Worst. 

With  these  explanations,  the  following  list  of  the  twelve 
valid  Affirmative  Moods  in  each  of  the  three  Figures,  and 
the  24  valid  Negative  Moods  in  the  First  Figure,  all  ex- 
pressed in  the  Hamiltonian  notation,  will  be  found  intel- 
ligible. 

In  this  Table,  the  Quantity  of  the  Conclusion  is  marked 
only  in  the  cases  already  considered,  wherein  the  Terms 
obtain  a  different  Quantity  from  that  which  they  held  in 
the  Premises;  accordingly,  when  not  marked,  the  quanti- 
fication of  the  Premises  is  held  as  repeated  in  the  Conclu- 
sion.    The  symbol  ,   placed   beneath  a   Conclusion, 

indicates  that,  when  the  Premises  are  converted,  the  Syllo- 
gism remains  in  the  same  Mood ;  ^x^  shows  that  the  two 
Moods  between  which  it  stands  are  convertible  into  each 
other  by  converting  their  Premises.  The  Middle  Term  is 
said  to  be  balanced,  when  it  is  Universal  in  both  Premises. 
The  Extremes,  or  Terms  of  the  Conclusion,  are  balanced, 
when  both  alike  are  distributed ;  unbalanced,  when  one  is, 
and  the   other  is  not,   distributed.      Accordingly,   of  the 


256 


MEDIATE  INFERENCE   OR   SYLLOGISM. 


B 


i.  C.- 

ii.  C,- 

iii.  C,- 

iy.  C:- 

t.  C,- 

vi.  C,- 

vii.  C  :- 


ix.  C:- 

x.  C:- 

xi.  C:- 
»■ 

xii.  C,- 


SCHEME  OF  NOTATION- 
TABLE  OF  SYLLO- 

A.    AFFIRMATIVE  MOODS. 

Fig.  i.  Fig.  ii. 


:M: 


:M: 


:M 


X 

.,M: 


:M, 


X 

i,M:. 


:M 


X 

viii.    C  , — —  :  M  : 


:M 


X 

i  ,M: 


Iff 


X 

i.M: 


>,r 


»,r 

v.T 
v.T 


■,r 


C,i 

c! 

c,! 

C,i 
C:i 

C,! 


M 


M 


M, 


X 


,M: 


M, 


X 


M 


M 


■,r 


X 


:  M 


:M  , 


X 


,  M 


:M 


X 


M 


Sots.  —  A.  1.  and  ii.  are  Balanced.    B.  The  other  moods  are  Unbalanced.    Of  these, 


THE  HAMILTONIAN   ANALYSIS. 


257 


FIGURED    SYLLOGISM. 
GISTIO     MOODS. 

A.    AFFIRMATIVE  MOODS. 

Fig.  hi. 


M 


M 


C, 


M, 


X 


,M 


X 


C, 


M: 


-,r 
-,r 


M 


X 


M 


C: 


M, 


X 


,M 


-:r 


,r 


X 


c, 


M: 


-.V 


B.    NEGATIVE  MOODS. 

Fig.  i. 


and  iv.  are  unbalanced  in  terms  only,  not  in  propositions  ;  the  rest  in  both. 


253  MEDIATE  INFERENCE   OR   SYLLOGISM. 

Moods  in  the  Table,  numbers  I.  and  II.  are  balanced  as 
respects  both  Terms  and  Propositions;  in  III.  and  IV., 
only  the  Terms  are  unbalanced;  in  the  remainder,  both 
Terms  and  Propositions  are  unbalanced. 

44  If  we  apply  the  Moods  to  any  Matter,  however  ab- 
stract, say  letters,  there  will  emerge  forty-two  Syllogisms ; 
for  the  formal  identity  of  the  balanced  Moods  will  then  be 
distinguished  b}  a  material  difference. "  Thus,  numbers  I. 
and  II.,  with  the  four  Negative  Moods  formed  from  them 
by  successively  negativing  each  of  their  Premises,  will, 
when  thus  treated,  yield  six  additional  Syllogisms,  making 
forty-two  in  all.  Take  for  instance,  number  I.,  Affirma- 
tive ;  when  each  of  its  Judgments  is  converted,  it  is  still 
in  the  same  Mood. 

Converting  each  Judgment. 
I.    All  rational  are  all  risible ;  All  risible  are  all  rational ; 

All  men  are  all  rational ;  All  rational  are  all  men  ; 

>.  All  men  are  all  risible.  .\  All  risible  are  all  men. 

44  On  the  contrary,  if  we  regard  the  mere  formal  equiv- 
alence of  the  Moods,  these  will  be  reduced  to  twenty-one 
reasonings,  —  seven  Affirmative  and  fourteen  Negative." 
Foi,  of  the  unbalanced  Moods,  every  odd  number  is  con- 
verted into  the  even  number  immediately  following;  and 
thus,  if  each  Mood  is  regarded  as  formally  equivalent  to  its 
converse,  (and  numbers  I.  and  II.  are  so  regarded  in  the 
Table,)  numbers  IV.,  VI.,  VIII,  X.,  and  XII.  must  be 
struck  out  of  the  enumeration,  and  only  seven  valid  Af- 
firmative Moods  remain.  In  like  manner,  in  Negatives, 
the  first  and  second  Moods  (a,  V)  of  the  pair  correspond- 
ing to  the  even  number  which  was  struck  out,  are  reduced 
from  or  to  the  second  and  first  Moods  (6,  «)  of  the  odd 
number  which  was  retained.  Five  pairs  being  thus  elim- 
inated, only  seven  pairs  —  fourteen  valid  Negative  moods 
--remain. 

Under  the  Aristotelic  doctrine,  as  we  have  seen,  logi- 


THE   HAMILTONIAN   ANALYSIS.  259 

cians  found  that  the  six  general  Rules,  which  they  had 
enounced  as  governing  all  Mediate  Inference,  did  not  suf- 
fice to  determine  which  of  the  Moods  were  valid,  and 
which  invalid,  in  each  of  the  four  Figures.  The  variations 
of  Figure  depend  upon  the  relative  position  of  the  Middle 
Term  as  Subject  or  Predicate  to  each  of  the  two  Terms 
of  the  Conclusion  ;  and  special  Rules  were  necessary  to 
prevent  these  variations  from  conflicting  with  the  two 
principles  which,  according  to  the  Aristotelians,  determine 
the  implicit  quantification  of  the  Predicate.  These  prin- 
ciples are,  —  1.  That  in  all  Affirmative  Judgments  the 
Predicate  is  Particular  ;  and,  2.  That  in  all  Negative  Judg- 
ments the  Predicate  is  Universal.  Now,  in  the  Second 
Figure,  the  Middle  Term  being  Predicate  in  both  Prem- 
ises, the  logicians  were  compelled,  in  order  to  prevent  the 
infringement  of  the  General  Rule,  that  the  Middle  Term 
7?iust  be  distributed  in  at  least  one  of  the  Premises,  to  enact 
the  Special  Rule,  that,  in  this  Figure,  one  of  the  Premises, 
and  consequently  the  Conclusion  also,  must  be  Negative. 
But  under  the  Hamiltonian  system  of  the  thorough-going 
quantification  of  the  Predicate,  since  the  Middle  Term  can 
be  distributed  when  it  is  the  Predicate  of  an  Affirmative, 
just  as  well  as  when  it  is  the  Predicate  of  a  Negative 
Judgment,  this  Special  Rule  is  both  useless  and  false. 
And  so  with  all  the  other  Special  Rules  for  each  of  the 
Figures.  They  are  needless,  because  they  were  formed 
only  on  the  supposition  that  the  Predicate  could  be  but 
partially  quantified  ;  they  are  false,  because  the  thorough- 
going quantification  of  the  Predicate  brings  to  light  many 
valid  forms  of  Syllogism  which  violate  each  of  these  rules. 

The  following  demonstration  of  the  falsity  of  these  Spe- 
cial Rules  is  borrowed  in  part  from  Mr.  Baynes's  "  New 
Analytic  of  Logical  Forms." 

The  Rules  of  the  First  Figure  are,  —  1.  That  the  Sump- 
tion must  be  Universal ;  2.  That  the  Subsumption  must 


260  MEDIATE   INFERENCE   OR   SYLLOGISM. 

be  Affirmative.     Quantify  the  Predicate,  and  neither  of 
these  holds  good. 

First  Rule  falsified. 

Some  men  are  some  fleet-footed  ; 
All  rational  is  all  man  ; 
.\  Some  rational  is  some  fleet-footed. 

Second  Rule  falsified. 

All  idealists  are  some  philosophers  ; 
No  sensualist  is  any  idealist ; 
•\  No  sensualist  is  some  philosopher. 

The  Rules  of  the  Second  Figure  are,  —  1.  That  one  of 
the  Premises  must  be  Negative ;  2.  That  the  Sumption 
must  be  Universal.  Both  are  abrogated  by  a  quantified 
Predicate,  thus :  — 

First  Rule  falsified. 

All  risible  is  all  man ; 
All  philosophers  are  some  men  ; 
•\  All  philosophers  are  some  risible. 

Second  Rule  falsified. 

Some  mortal  is  all  man  ; 
All  rational  is  all  man  ; 
.*.  All  rational  is  some  mortal. 

The  Rules  of  the  Third  Figure  are,— -1.  That  the  Sub- 
sumption  must  be  Affirmative ;  2y  That  the  Conclusion 
must  be  Particular. 

First  Rule  falsified. 

All  free  agents  are  all  responsible ; 
No  free  agent  is  any  brute  ; 
.\  No  brute  is  any  responsible. 

Second  Rule  falsified. 

All  triangles  are  halves  of  parallelograms  ; 
All  triangles  are  all  trilaterals  ; 
.*.  All  trilaterals  are  halves  of  parallelograms. 

All  the  Special  Rules  being  thus  abrogated,  the  unity 


THE   HAMILTONIAN   ANALYSIS.  261 

and  simplicity  of  the  Syllogistic  process  become  manifest. 
Hamilton's  Supreme  Canon,  which  is  a  mere  compend  of 
the  six  General  Rules,  appears  as  the  universal  and  all- 
sufficient  law  of  Mediate  Inference,  and  the  science  of 
Logic  is  freed  from  the  encumbrance  of  a  mass  of  needless 
distinctions  and  superfluous  details.  As  Figure  is  demon- 
strated to  be  an  unessential  variation,  all  the  Rules  for 
Reduction  are  swept  away.  In  fact,  the  process  of  Reduc- 
tion is  so  far  simplified  by  allowing  all  Judgments  to  be 
converted  simply,  that,  if  we  still  need  to  have  recourse  to 
it  in  order  that  the  reasoning  may  appear  in  its  most  ob- 
vious and  natural  form,  the  requisite  changes  suggest  them- 
selves, and  the  work  may  be  performed  without  the  aid  of 
rules. 

Some  observations  are  necessary,  however,  in  respect  to 
the  applicability  of  the  different  Figures  to  those  two  di- 
rections of  the  reasoning  process  which  are  called  Deduc- 
tive and  Inductive.  This  subject  has  been  so  well  ex- 
plained by  Mr.  Baynes,  that  I  borrow  his  language.  We 
have  seen  that  the  characteristic  of  reasoning  in  Intension 
—  or  Comprehension,  as  it  is  more  frequently  called  —  is, 
that  the  Predicate  is  contained  in  the  Subject ;  of  reason- 
ing in  Extension,  that  the  Subject  is  contained  under  the 
Predicate.  "  This  being  remembered,"  says  Mr.  Baynes, 
"  it  will  appear  that  in  the  Second  Figure,  where  the  Mid- 
dle Term  as  Predicate  contains  both  the  Subjects  under  it, 
Extension  will  predominate.  In  the  Third,  where  the  Mid- 
dle Term  as  Subject  is  contained  under,  and  therefore  com- 
prehends in  it  both  the  Predicates,  Comprehension  will  pre- 
vail. In  the  First  Figure,  again,  where  the  Middle  Term 
is  both  Subject  and  Predicate,  Extension  and  Comprehen- 
sion balance  each  other.  The  First  Figure  is  indifferently 
competent  to  either. 

"Reasoning,  however,  proceeds  not  only  in  different 
wholes,  but  in  different  aspects  of  the  same  whole.     We 


262  MEDIATE  INFERENCE   OR   SYLLOGISM. 

may,  it  is  evident,  regard  any  whole,  considered  as  the 
complement  of  its  parts,  in  either  of  two  ways  ;  for  we 
may,  on  the.  one  hand,  look  from  the  whole  to  the  parts. 
and  reason  accordingly  downwards ;  or,  on  the  other 
hand,  look  from  the  parts  to  the  whole  they  constitute, 
and  reason  accordingly  upwards.  The  former  of  these 
reasonings  is  called  Deductive,  the  latter  Inductive.  De- 
ductive reasoning  is  founded  on  the  maxim,  ■  What  be- 
longs to  the  containing  whole  belongs  also  to  the  con- 
tained parts ' ;  Induction,  on  the  contrary  maxim,  4  What 
belongs  to  the  constituent  parts  belongs  also  to  the  con- 
stituted whole.'  Thus,  in  Deductive  reasoning,  the  whole 
is  stated  first,  and  what  is  affirmed  of  it  is  affirmed  of  the 
parts  it  contains ;  in  other  words,  a  general  law  is  laid 
down,  and  predicated  of  the  particular  instances  to  which 
it  applies.  In  Inductive  reasoning,  the  parts  are  first  stated, 
and  what  is  predicated  of  them  is  also  predicated  of  the 
whole  they  constitute ;  in  other  words,  the  particular  in- 
stances are  first  stated  as  facts,  and  then  the  law  they  con- 
stitute is  evolved. 

"  This  being  the  nature  of  these  counter  and  correlative 
reasonings,  it  appears  to  us,  that,  though  each  kind  is  com- 
petent in  either  whole  (Extension  or  Comprehension),  yet 
the  reasoning  in  the  whole  of  Extension  is  more  naturally 
allied  to  the  Deductive,  and  that  in  Comprehension  to  the 
Inductive.  For,  in  the  whole  of  Extension,  the  reason- 
ing proceeds  from  the  general  to  the  special,  —  from  the 
abstract  to  the  concrete,  —  from  general  laws  to  the  par- 
ticular instances  which  are  contained  under  them ;  while 
in  that  of  Comprehension,  on  the  other  hand,  the  reasoning 
proceeds  from  the  special  to  the  general,  —  from  the  con- 
crete to  the  abstract,  —  from  the  particular  instances  to  the 
general  laws,  whose  operation  they  exemplify. 

"  Considering  these  kinds  of  reasoning  in  relation  to  the 
Figures,  it  will  appear,  then,  that  since  Extension  prevails 


THE   HAMILTONIAN   ANALYSIS.  263 

in  t\ie  Second,  that  will  be  so  far  more  suitable  for  Deduc- 
tive reasoning;  and  since  Comprehension  prevails  in  the 
Third,  that  Figure  will  so  far  be  more  adapted  for  Induc- 
tive reasoning ;  while,  since  Extension  and  Comprehension 
prevail  equally  in  the  First,  that  Figure  will  be  equally 
fitted  for  either  kind  of  reasoning. 

"  The  relation  of  the  Figures  to  these  different  kinds  of 
reasoning  will  be  best  illustrated  by  an  example.  We  will 
take  first  the  Second  Figure  :  — 

Fig.  II. 
Deductive  Reasoning  :   Quantity  of  Extension. 
Endowed  with  reason  is  all  man. 
European,  Asiatic,  African,  American,  are  all  man. 
European,  Asiatic,  African,  American,  are  endowed  with  reason. 

"Here  the  reasoning  is  Deductive,  for  the  law  is  first 
enounced,  the  individual  instances  are  next  brought  under 
it,  and  it  is  then  affirmed  of  them  ;  it  is  Extensive,  for  it 
proceeds  from  the  wider  notion  through  the  narrower  to 
the  individual.  Let  us  now  take  the  same  Terms  and  treat 
them  Inductively,  beginning  with  the  individuals.  The 
reasoning  will  then  be  in  the  whole  of  Comprehension,  and 
will  naturally  appear  in  the  form  of  the  Third  Figure :  — 

Fig.  III. 
Inductive  Reasoning :  Quantity  of  Comprehension. 
European,  Asiatic,  African,  American,  are  all  man. 
European,  Asiatic,  African,  American,  are  endowed  with  reason. 
Endowed  with  reason  is  all  man. 

"  Here  the  reasoning  is  Inductive,  for,  beginning  with  the 
individuals  in  the  Premises,  we  arrive  at  the  law  (with 
which  we  started  in  the  previous  Syllogism)  in  the  Conclu- 
sion ;  it  is  Comprehensive  or  Intensive,  for  it  proceeds  from 
the  concrete  to  the  abstract,  from  a  greater  totality  of  attri- 
bute to  a  less.  In  other  words,  in  either  Quantity  (Exten- 
sive or  Intensive),  we  reason  from  the  greatest  whole  ;  but 


264  MEDIATE  INFERENCE   OR   SYLLOGISM. 

in  the  Quantity  of  Extension,  the  greatest  whole  is  the  most 
abstract  notion  (i.  e.  the  widest  law),  whereas  in  that  of 
Comprehension,  the  greatest  whole  is  the  most  concrete 
notion  (i.  e.  the  individual  instance).  But  proceeding 
thus  from  the  widest  law,  the  reasoning  is  necessarily 
Deductive,  while  on  the  other  hand,  proceeding  from  the 
individual  instance,  it  is  as  necessarily  Inductive. 

"  We  may  give  the  same  example  in  the  First  Figure,  to 
illustrate  (what  will  now  be  quite  obvious)  that  it  is  in- 
differently competent  to  either  reasoning  :  — 

Fig.  I. 
Deductive  Reasoning  :  Quantity  of  Extension. 
All  man  is  endowed  with  reason. 
European,  Asiatic,  African,  American,  are  all  man. 
European,  Asiatic,  African,  American,  are  endowed  with  reason. 

Inductive  Reasoning  :   Quantity  of  Comprehension. 
P^uropean,  Asiatic,  African,  American,  are  all  man. 
All  man  is  endowed  with  reason. 
European,  Asiatic,  African,  American,  are  endowed  with  reason. 

"  The  Second  and  Third  Figures  are  indeed  naturally 
respectively  connected  with  Deductive  and  Inductive  rea- 
soning; for  in  the  Second,  we  judge  the  likeness  or  unlike- 
ness  of  two  parts,  as  they  are  contained  or  not  contained  by 
a  common  whole  ;  while  in  the  Third,  we  judge  the  likeness 
or  unlikeness  of  two  wholes,  as  they  severally  contain  or 
do  not  contain  common  parts." 

In  respect  to  Hypothetical  and  Disjunctive  reasoning, 
Hamilton  has  followed  Kant  in  declaring  that  all  Mediate 
Inference  is  one,  —  that  which  has  been  denominated  Cate- 
gorical ;  all  the  so-called  Conditional  Syllogisms  are  reduci- 
ble to  Immediate  Inferences.  Their  characteristic  feature 
is,  that  they  have  no  Middle  Term  ;  the  agreement  or  dis- 
agreement of  the  two  Terms  of  the  Conclusion  with  each 
other  is  ascertained,  not  by  comparing  each  of  them  sep- 
arately with  a  third  Term,  which  is  a  mediate  process,  but 


THE  HAMILTONIAN  ANALYSIS.  265 

directly,  from  a  single  Premise,  here  incorrectly  styled  a 
Major  Premise.  This  Premise  consists,  not  of  two  Terms 
merely,  but  of  two  Judgments,  called  respectively  the  Ante- 
cedent and  the  Consequent ;  a  relation  of  mutual  depend- 
ence is  affirmed  to  exist  between  these,  by  virtue  of  which 
the  Axiom  of  Reason  and  Consequent  becomes  applicable 
to  the  case.  This  Axiom,  as  has  been  shown  (page  54), 
13  lirectly  explicated  into  the  two  Laws,  —  1.  That  to  affirm 
the  Reason  or  the  Condition  is  also  to  affirm  the  Consequent ; 
and,  2.  That  to  deny  the  Consequent  is  also  to  deny  the 
Reason.  A  ratione  ad  rationatum,  a  negatione  rationati  ad 
negationem  rationis,  valet  consequentia.  The  single  Prem- 
ise affirming  that  this  relation  of  Reason  and  Consequent 
exists  between  the  Judgments  which  are  its  two  parts,  this 
Axiom  compels  us  to  infer  immediately,  or  without  the  aid 
of  a  third  Term,  both  that  the  Consequent  follows  when 
the  Antecedent  is  posited,  and  that  the  Antecedent  is  de- 
nied when  the  Consequent  is  sublated. 

The  reduction  of  a  Hypothetical  Judgment  to  a  Cate- 
gorical shows  very  clearly  the  Immediacy  of  the  reasoning 
in  what  is  called  a  Hypothetical  Syllogism.  Thus,  If  A  is 
B,  C  is  D,  is  equivalent  to 

All  cases  of  A  is  B  are  cases  of  C  is  D. 
Some  cases  of  A  is  B  are  cases  of  )  p  .    j^ 
This  case  of  A  is  B  is  a  case  of      J 

In  such  reasoning,  as  Kant  remarks,  the  Premise  does 
not  afford  a  proof  of  the  Conclusion,  but  a  ground  or  man- 
ner of  proving  it ;  it  is  then  only  an  explication  of  the 
meaning  of  the  Premise,  when  we  say  that  the  Consequent 
holds  good  when  the  ground  or  Reason  exists,  and  that  the 
Reason  does  not  exist  if  the  Consequent  does  not  hold 
good.  Hence,  this  kind  of  reasoning  may  properly  be 
referred  to  the  doctrine  of  Exponibles.  All  the  Matter 
which  we  are  reasoning  about  is  embraced  in  the  one  com- 
plex proposition  that  is  here  called  the  Premise  ;  and  all 

12 


260  MEDIATE  INFERENCE   OR   SYLLOGISM. 

that  the  reason er  has  to  do  is  to  explicate  or  interpret  this 
proposition.  Considered  as  an  Exponible,  the  Conditional 
Judgment,  If  A  is  B,  C  is  2),  may  be  interpreted  in  two 
ways,  —  1.  as  a  Restrictive;  2.  as  an  Exclusive.  The 
first  of  these  interpretations  yields,  by  the  Immediate  In- 
ference of  Subalternation,  what  is  called  the  Modus  ponens 
of  Conditional  Reasoning ;  the  second  yields,  also  Imme- 
diately, the  Modus  tollens. 

1.  Thus,  Restrictively,  in  affirming  that,  if  A  is  B,  C  is 
D,  we  do  not  say,  C  is  always  D,  but  only,  "  All  C,  when 
A  is  By  is  D,"  the  italicized  clause  being  the  Restriction, 
and  answering  to  a  limiting  adjective,  —  say,  yellow  :  All 
yellow  C  is  2).     Their,  by  Subalternation, 


Some  yellow  C  )  •    -^ 
This  yellow  C    ) 


Again,  the  same  Judgment,  If  A  is  B,  C  is  2),  yields,  by 
the  Immediate  Inference  of  Contraposition,  If  C  is  not  2), 
A  is  not  B.     This  is  an  Exclusive  ;  it  affirms  that 
A  is  B  only  when  C  is  D  ;  then,  Immediately, 
A  is  not  B  when  C  is  not  D. 
In  fact,  all  reasoning  is  hypothetical ;  the  Syllogism,  as 
such,  does  not  affirm  its  Conclusion  absolutely,  but  only  its 
dependence  on  the  Premises.     If  the  Premises  are  true, 
the  Conclusion  follows.     Any  Immediate  Inference,  also, 
may  be  stated  hypothetically.     Take  that  by  Subalterna- 
tion, for  instance  :  — 

All  A  is  B  ; 
.*.  Some  A  is  B. 

Stated  hypothetically  thus  :  — 

If  all  A  is  B,  some  A  is  B  ; 
.*.  Some  A,  or  this  A,  is  B. 

It  is  unnecessary  to  consider  separately  the  case  of  Dis- 
junctive reasoning ;  for  it  has  already  been  proved  (page 
131)  that  Disjunctives  are  only  complex  Hypotheticals. 


OF  FALLACIES.  267 


CHAPTER    IX 


OF   FALLACIES. 


A  FALLACY  is  any  instance  of  unsoun;l  or  invalid 
reasoning  which  has  a  deceptive  appearance  of  cor- 
rectness and  truth.  If  it  be  such  that  the  writer  or  speaker 
is  himself  deceived  by  it,  it  is  called  a  Paralogism  ;  if 
framed  by  him  for  the  purpose  of  deceiving  others,  while 
he  is  himself  aware  of  its  unsoundness,  it  is  a  Sophism. 
Those  of  the  former  class  are  what  we  have  most  to  dread . 
for  on  account  of  the  necessary  dependence  of  Thought  ou 
Language,  we  often  commit  them  in  our  silent  meditations, 
while  we  are  attempting  to  discover  the  truth  or  to  dis- 
intricate  it  from  error.  The  danger  is  greatly  enhanced 
by  the  symbolic  or  algebraic  use  of  Language,  whereby 
we  employ  words  for  the  moment  as  mere  signs,  without 
spreading  out  their  signification  before  the  mind,  and  thus 
are  often  deceived  by  their  ambiguity  and  vagueness. 
Sophisms  are  comparatively  of  rare  occurrence,  as  one 
who  wishes  to  deceive  can  do  so  more  easily  and  effect- 
ually by  false  statements  than  by  false  reasonings.  It  is 
more  difficult  to  weave  invalid  but  specious  arguments, 
knowing  their  incorrectness,  than  to  reason  correctly  from 
wrong  premises.  Formerly  it  was  otherwise  ;  the  great 
use  of  disputation  by  the  ancient  sophists  and  the  School- 
men, as  a  logical  exercise  and  a  means  of  education,  tended 
to  create  a  special  art  of  sophistry,  and  has  left  on  record  a 
multitude  of  logical  puzzles  for  the  amusement  of  later 
times.      Dexterity  in  framing  and  solving  these  sophisms 


268  OF   FALLACIES. 

was  reckoned  a  scholarly  accomplishment,  and  one  of  the 
special  fruits  of  a  university  education.  Nowadays  this 
species  of  mental  gymnastics  has  fallen  into  entire  disre- 
pute, as  men  prefer  to  sharpen  their  wits  on  graver  matters 
and  subjects  of  more  immediate  interest. 

The  purpose  of  the  doctrine  of  Fallacies,  as  it  is  now 
taught,  is  to  familiarize  the  mind  with  those  instances  of 
erroneous  reasoning  which  are  most  likely  to  lead  our  own 
thoughts  astray  in  the  search  after  truth  and  the  elimina- 
tion of  error.  For  this  end,  a  classification  of  Fallacies  is 
desirable.  The  earliest  attempt,  of  which  we  have  any 
distinct  knowledge,  thus  to  reduce  them  to  system,  was 
that  of  Aristotle;  and  the  chief  endeavor  of  later  logicians 
has  been  to  ascertain,  develop,  and  illustrate  his  meaning. 
Even  the  phraseology  which  he  employed  became  conse- 
crated, as  it  were,  by  long  use  in  the  Schools ;  and  the 
chief  dispute  among  modern  writers  has  been,  whether  a 
particular  Fallacy  is  rightly  designated  by  this  or  that  tech- 
nical name.  A  more  unprofitable  logomachy  can  hardly 
be  imagined.  Our  business  is  to  teach  Logic,  and  not  to 
write  a  commentary  upon  Aristotle.  The  classification 
framed  by  him,  though  a  marvellous  work  for  the  time, 
evincing  the  prodigious  acuteness  and  comprehensiveness 
of  view  for  which  his  intellect  was  so  remarkable,  must 
still,  if  viewed  under  the  lights  of  modern  science,  be  re- 
garded as  crude  and  imperfect.  A  better  arrangement  can 
be  effected,  not  by  laying  aside  his  phraseology  altogether, 
but  by  employing  his  technical  terms,  when  they  are  con- 
venient, under  the  conventional  meaning  which  has  long 
been  assigned  to  them,  and  by  striking  out  many  of  his  dis- 
tinctions, and  introducing  others  in  their  place  which  have 
been  suggested  by  later  experience.  The  use  of  classifica- 
tion, it  must  be  remembered,  is  merely  subsidiary  ;  the 
main  purpose  is  to  become  familiar  with  the  character- 
istics of  those  forms  of  erroneous  reasoning  which  most 


OF  FALLACIES.  269 

frequently  occur  in  practice ;  and  this  can  be  best  accom- 
plished by  dividing  them  into  species,  and  discriminating 
these  species  from  each  other. 

It  should  be  observed  that,  strictly  speaking,  the  consid- 
eration of  Fallacies  is  extralogical.  We  have  already  laid 
down  the  Rules  of  correct  or  valid  Inference ;  any  argu- 
mentation which  violates  one  or  more  of  these  Rules  is  in- 
valid. But  an  open  violation  of  one  of  them,  as,  from  its 
very  obviousness,  it  is  not  likely  to  deceive  anybody,  is  not 
usually  called  a  Fallacy.  A  classification  of  what  are  prop- 
erly denominated  Fallacies  would  depend  on  an  enumera- 
tion of  those  circumstances  which  are  most  likely  to  deceive 
us  —  to  cover  up  the  violation  of  a  Rule  —  in  the  forma- 
tion of  our  Judgments  and  Inferences;  and  a  disquisition 
on  these  circumstances  would  form  a  valuable  chapter  of 
Psychology,  or  in  a  Treatise  on  the  practical  Conduct  of 
the  Understanding.  The  chief  source  of  these  errors  is 
the  ambiguity  of  language,  both  as  respects  the  meaning 
of  single  words  (cequivocatid)  and  the  construction  of 
sentences  (amphibolic?).  Then  the  ultimate  remedy  for 
them  is  to  be  found  in  the  study  of  language ;  it  would  be 
a  part  of  the  doctrine  of  Hermeneutics,  or  the  science  of 
Interpretation.  But  as  certain  prominent  classes  of  them 
frequently  perplex  and  vitiate  our  reasonings,  a  description 
of  such  is  not  entirely  out  of  place  as  an  appendage  to  the 
science  of  Logic. 

We  observe  in  the  first  place,  then,  that  Aristotle  was 
wrong,  and  his  authority  has  misled  most  of  the  later  logi- 
cians, in  forming  a  distinct  class  of  the  Fallacies  of  language. 
His  first  distinction  is  between  those  in  dictione,  which 
arise  merely  from  the  improper  use  of  words  as  arbitrary 
signs  of  thought,  and  which,  therefore,  generally  disappear 
when  the  proposition  is  translated  into  another  language, 
and  those  extra  dictionem,  which  are  in  the  Thought  iteelf, 
whether  in  its  Matter  or  its  Form,  and  therefore  adhere  to 


270  OF   FALLACIES. 

the  Thought,  however  it  may  be  expressed.  He  enumer- 
ates six  classes  or  subdivisions  of  the  former;  but  the 
division  is  a  faulty  one,  as  the  six  can  be  reduced  to  two, 
namely,  the  ambiguity  of  single  words,  or  the  ambiguous 
construction  of  sentences.  But  we  object  generally,  that 
the  erroneous  use  of  language  is  of  no  logical  import  what- 
ever, if  it  be  not  employed  to  hide  some  defect  in  the  rea- 
soning. The  ambiguity  of  words  may  cloak,  but  does  not 
constitute,  the  sophism.  If  the  suspected  Syllogism  does 
not  contain  an  undistributed  Middle,  or  four  Terms  instead 
of  three,  or  an  Illicit  Process,  or  some  other  violation  of 
logical  Rule,  it  is  a  sound  Inference,  however  faulty  may 
be  the  language  in  which  it  is  expressed.  Accordingly,  it 
will  be  found,  that  all  the  instances  given  in  the  books  to 
illustrate  the  six  classes  of  what  may  be  briefly  termed 
Verbal  Fallacies,  resolve  themselves,  when  the  ambiguity 
is  detected,  into  logical  quadrupeds,  as  Syllogisms  with/bur 
Terms  have  been  derisively  called,  or  some  other  form  of 
violating  one  or  more  of  the  Canons  of  Pure  Logic.  Take 
the  following  illustration,  from  Mr.  De  Morgan,  of  the  Fal- 
lacy of  ambiguous  words,  Aristotle's  first  subdivision. 

All  criminal  actions  ought  to  be  punished  by  law ; 

Prosecutions  for  theft  are  criminal  actions ; 

Therefore,  prosecutions  for  theft  ought  to  be  punished  by  law. 
Here  the  Middle  Term,  criminal  actions,  is  ambiguous ;  in 
the  Sumption,  it  means  immoral  deeds ;  in  the  Subsump- 
tion,  it  is  a  technical  phrase  for  a  particular  class  of  legal 
'proceedings.  Substitute  these  definitions  for  the  phrar,e 
defined,  and  it  is  apparent  that  the  pretended  Syllogism  is 
a  quadruped. 

Take  the  following  as  an  instance  of  Aristotle's  second 
subdivision,  —  ambiguous  construction. 

All  that  glitters  is  not  gold  ; 

Tinsel  glitters ; 

Then,  tinsel  is  not  gold. 


OF  FALLACIES.  271 

Here,  in  the  Sumption,  the  Middle  Term  is  apparently 
distributed  by  the  predesignation  all ;  but  it  is  not  so  in 
reality,  as  the  negative  particle  ought  to  be  construed  as 
qualifying  all,  and  not^all_  means  some  are  not.  But  if  we 
read,  Some  things  that  glitter  are  not  gold,  the  Middle  is  not 
distributed  in  either  Premise. 

The  class  of  Verbal  Fallacies,  then,  should  be  abolished, 
as»  all  instances  of  invalid  or  erroneous  reasoning,  being 
either  an  open  or  a  concealed  violation  of  the  Laws  of 
Thought,  are  necessarily  extra  dictionem,  or  independent  of 
language.  Then  the  most  general  division  of  them  will  be 
into  Formal  and  Material  Fallacies,  "according  as  the 
source  of  deception  lies  in  the  act  of  Thought  itself,  or  in 
the  object  upon  which,  or  the  circumstances  under  which, 
it  is  exercised."  This  distinction  may  be  well  expressed 
by  saying  that,  in  every  Fallacy,  the  Conclusion  either 
does,  or  does  not,  follow  from  the  Premises.  If  it  does  not  so 
follow,  it  is  clear  that  the  fault  is  in  the  reasoning,  and  in 
that  alone  ;  the  error  concerns  only  the  Form  of  Thought, 
so  that  these  alone  are  Logical  Fallacies  strictly  so  called. 
If  the  Conclusion  does  follow  from  the  Premises,  we  must 
search  for  the  deception  in  the  Matter  of  the  Thought ; 
that  is,  we  must  consider  what  we  are  reasoning  about, 
and  what  is  the  Conclusion  which  we  wish  to  establish. 
Such  consideration  is  properly  extralogical ;  but  as  the  pur- 
pose of  examining  both  classes  of  these  Fallacies  is  the 
same,  namely,  to  guard  the  mind  against  error  in  its  own 
processes,  and  as  the  consideration  of  only  one  class  of  Fal- 
lacies would  very  imperfectly  answer  this  end,  we  subordi- 
nate strict  method  to  convenience,  and  take  into  view  all 
cases  of  defective  and  sophistical  argumentation.  While 
considering  both  of  these  classes  of  Fallacies,  the  ambi- 
guities of  language  which  hide  them,  and  which  originally 
led  the  reasoner  astray,  will  incidentally  come  into  notice, 
and  the  exposure  of  them  thus  effected  will  be,  in  a  prac- 


272  OF  FALLACIES. 

tical  point  of  view,  the  most  valuable  result  of  the  discus- 
sion. 

The  subdivision  of  Fallacies  in  the  Form  of  Thought, 
the  Conclusion  being  illogically  drawn,  is  easily  effected, 
as  it  must  have  reference  to  the  six  General  Rules,  which 
are  all  embodied  in  Hamilton's  one  Supreme  Canon  of 
Mediate  Inference.  But  the  classification  thus  made  is  not 
easily  adhered  to,  as  it  will  often  be  found  that  the  same 
Fallacy  involves  a  violation  of  two  or  more  of  these  Gen- 
eral Rules.  The  subject  being  once  properly  distributed 
into  parts,  however,  the  question  is  of  little  moment 
whether  a  particular  case  is  rightly  assigned  to  this  or  that 
class,  if  it  may  fairly  be  placed  under  either.  The  Rules 
most  frequently  violated  are  those  which  require,  —  1.  That 
a  Syllogism  should  consist  of  only  three  Terms ;  2.  That 
the  Middle  Term  should  be  distributed  in  at  least  one  of 
the  Premises  ;  3.  That  neither  Term  can  be  distributed  in 
the  Conclusion,  if  it  was  not  taken  universally  in  the  Prem- 
ises ;  4.  That  the  Conclusion  must  be  Negative,  if  either 
Premise  is  Negative ;  5.  That  at  least  one  Premise  must 
be  Affirmative.  Besides  the  five  kinds  of  Fallacies  arising 
from  violations  of  these  Rules,  two  others  should  be  men- 
tioned, being  the  two  invalid  Moods  of  Hypothetical  In- 
ference :  —  6.  From  denying  the  Antecedent,  or,  7.  From 
affirming  the  Consequent,  no  Conclusion  can  be  drawn.  A 
number  of  other  classes  might  be  framed,  arising  from  vio- 
lation of  the  various  Rules  of  Immediate  Inference,  —  the 
Laws  of  Conversion,  Opposition,  Infinitation,  for  instance. 
But  as  such  errors  are  neither  frequent  nor  insidious,  they 
need  not  be  considered  here. 

1.  To  the  class  of  Syllogisms  which  are  invalid  because 
they  consist  of  more  than  three  Terms  may  be  referred  all 
the  cases  which  are  usually  placed  under  the  head  of  ambig- 
uous Middle.  If  an  ambiguous  word  or  phrase  is  employed 
as  the  Middle  Term  in  the  Major  Premise  in  one  of  its 


OF  FALLACIES.  27  S 

significations,  and  in  the  Minor  Premise  in  a  different  sig- 
nification, it  is  evident  that  it  does  not  afford  us  any  means 
of  ascertaining  the  relation  of  the  Extremes  to  each  other. 
Having  only  compared  A  with  M,  and  B  with  N,  we  can- 
not tell  whether  A  is,  or  is  not,  B.  Cases  of  this  Fallacy 
are  more  numerous,  and  more  apt  to  deceive,  than  those 
of  any  other  class.  They  are  the  more  insidious,  because 
terms  in  frequent  use,  and  which  are  constantly  employed 
by  the  vulgar  in  ordinary  conversation,  are  precisely  those 
which  are  most  apt  to  become  ambiguous  ;  but  on  account 
of  their  familiarity,  we  fancy  that  we  are  perfectly  ac- 
quainted with  them,  and  therefore  never  suspect  that  they 
are  leading  us  astray. 

Most  political  Fallacies  are  of  this  order.  That  very 
common  phrase,  the  government,  means  both  "  the  system 
of  laws  under  which  we  live  and  the  machinery  by  which 
these  are  administered,"  and  "  the  members  of  the  ad- 
ministration for  the  time  being,  whose  duty  it  is  to  carry 
out  this  system  and  to  work  this  machinery  " ;  or  it  may 
mean  certain  measures,  or  a  favorite  policy,  of  these  admin- 
istrators. Hence  what  Jeremy  Bentham  calls  u  the  official 
malefactor's  screen  " ;  —  "  Attack  us,  you  attack  the  gov- 
ernment." It  may  well  happen  that  we  best  manifest  our 
attachment  to  the  government  in  the  former  sense,  by  a 
vehement  opposition  to  it  in  the  second  meaning  ;  or,  if  the 
administrators  are  really  able  and  well  disposed,  but  are 
pursuing  a  mistaken  policy  in  one  respect,  that  we  best 
show  our  regard  for  them  personally,  by  laboring  to  con- 
vince them  of  their  error. 

Still  more  ambiguous  is  that  which  is  so  much  talked  and 
written  about,  —  the  Church.  How  many  controversies 
might  have  been  spared,  and  how  many  volumes  remained 
unwritten,  had  it  been  remembered  that,  at  least  in  all 
countries  where  a  religious  establishment  exists  supported 
by  law,  "  the  Church "  may  have  these  six  different 
12*  B 


274  OF  FALLACIES. 

meanings :  —  1.  a  place  of  meeting  for  worship  ;  2.  all  the 
people  engaged  as  worshippers  ;  3.  only  the  faithful  who,  in 
in  every  age,  since  the  advent  of  the  Redeemer,  have 
constituted  the  mystical  Body  of  Christ;  4.  the  inferior 
clergy  by  whom  the  ceremonies  of  worship  are  conducted ; 
5.  the  superior  clergy,  who  may  be  regarded  as  the  heads 
of  the  Church  ;  6.  rules  and  customs  respecting  the  modes 
of  worship.  As  Bentham  remarks,  church  is  often  made  to 
mean  churchmen,  and  law  to  signify  lawyers,  by  the  easy 
device  of  "substituting  for  men's  proper  official  denom- 
ination the  name  of  some  fictitious  entity,  to  whom,  by 
customary  language,  and  hence  opinion,  the  attribute  of 
excellence  has  been  attached." 

If  it  were  allowable  to  make  a  new  use  of  one  of  Bacon's 
technical  appellations,  another  large  class  of  these  sophisms 
might  be  called  Fallacies  of  the  Forum.  These  relate 
chiefly  to  money,  currency,  prices,  interest,  profits,  and 
other  terms  of  frequent  use  in  commercial  and  financial 
transactions.  Money  may  mean  either  specie,  or  bank-notes, 
or  currency  consisting  of  a  mixture  of  these  two,  or  credit, 
or  capital,  or  that  portion  of  capital  which  is  offered  for  loan. 
An  individual  merchant  is  said  to  be  in  want  of  money 
wherewith  to  pay  his  debts,  when  his  only  real  lack  is  of 
credit,  capital,  or  merchandise,  money  serving  no  other 
purpose  in  the  affair  than  that  of  the  carts  by  which  the 
merchandise  is  transported.  Again,  interest  is  usually 
spoken  of  as  if  it  were  the  interest  of  money ;  whereas  a 
little  reflection  will  satisfy  any  one,  that  money  (if  the 
name  be  applied,  as  it  usually  is,  to  specie,  to  bank-notes, 
or  to  a  combination  of  the  two)  yields  neither  profit  nor 
interest ;  whether  it  is  in  the  hands  of  an  individual  or  a 
corporation,  whether  in  the  pocket  or  in  a  safe,  it  is  a  part 
of  the  owner's  dead  capital,  and  therefore  he  usually  aims 
to  get  along  with  the  use  of  as  little  of  it  as  possible. 
A^ain,  money  is  usually  considered  as   the   measure   of 


OF   FALLACIES.  2lb 

wealth ;  and  then,  by  a  very  common  metonomy,  the  meas- 
ure is  confounded  with  the  thing  measured.  Hence  the 
following  sophism,  which  may  be  said  to  have  directed  the 
commercial  legislation  of  all  civilized  countries,  down,  at 
least,  to  the  time  of  Adam  Smith. 

Any  increase  of  the  money  in  a  country  is  an  equivalent  enlarge- 
ment of  its  wealth. 

Laws  to  protect  native  manufactures  against  foreign  competition 
tend  to  increase  the  money  in  the  country. 

Therefore,  such  laws  tend  to  increase  the  nation's  wealth. 

But  Adam  Smith  demonstrated  that  laws  directed  solely  to 
keeping  specie  at  home,  only  tend  to  make  the  country 
poorer  ;  and  his  arguments  being  at  last  generally  admitted 
to  be  conclusive,  there  arose  the  opposite  Fallacy  of  uni- 
versal Free  Trade,  which  now  controls  the  legislation  of 
England,  and  is  gaining  ground  in  many  other  quarters. 

Laws  which  do  not  increase  the  quantity  of  money  in  the  coun- 
try are  at  best  useless. 
A  Protective  System  does  not  increase  this  quantity. 
Therefore,  a  Protective  System  is  useless. 

Of  course,  the  answer  to  this  argument  is,  that  measures 
which  do  not  prevent  specie  from  going  abroad  may  yet 
make  the  people  more  wealthy  and  prosperous,  by  ena- 
bling them,  in  their  foreign  trade,  to  exchange  manufactures 
for  raw  material,  —  that  is,  the  products  of  skilled  labor 
for  those  of  rude  labor,  —  that  is,  again,  the  fruits  of  the 
industry  of  one  man  for  those  of  the  industry  of  three  or 
four  men.  And  it  is  precisely  this  system,  —  fostering  the 
growth  of  native  manufactures  and  allowing  the  produc- 
tion of  raw  material  to  take  care  of  itself,  —  and  not  the 
prevalence  of  the  doctrine  of  Free  Trade,  which  has  been 
the  great  source  of  England's  prosperity. 

Another  frequent  source  of  this  Fallacy  —  the  introduc- 
tion, through  the  ambiguity  of  language,  of  four  Terms  into 


276  OF  FALLACIES. 

a  Syllogism — is  the  doctrine  that  the  primary  or  etymo- 
logical meaning  of  a  word  is  its  only  proper  signification,  or 
that  it  is  the  standard  to  which  modern  usage  ought  to  con- 
form. This  sophism  is  the  more  frequent,  as  it  affords  an 
opportunity  for  a  little  display  of  erudition ;  numerous 
instances  of  it  can  be  found  in  what  is  otherwise  an  ingeni- 
ous  and  excellent  work,  Tooke's  "  Diversions  of  Turley." 
Thus,  right  comes  from  rectus,  and  that  from  rego,  —  to 
rule  or  govern ;  hence  an  alleged  confirmation  of  the  doc- 
trine of  Hobbes,  that  right  is  only  a  creature  of  positive 
law,  another  unfounded  assumption  being  then  allowed  to 
slip  in,  that  the  only  kind  of  law  is  human,  not  divine. 
Again,  most  of  the  words  which  are  now  significant  of  the 
operations  of  Mind  were  originally  applied  to  some  of  the 
forms  or  changes  of  Matter ;  and  this  fact  has  heen  held  to 
countenance  the  doctrine  of  materialism.  But  that  spirit 
once  signified  breath,  and  animus,  ave/Aos,  air,  does  not 
afford  even  a  presumption  that  such  is  their  present  mean- 
ing. The  secondary  or  usual  sense  of  a  word  has  often 
travelled  so  far  away  from  its  primitive  application  as  to 
have  lost  sight  of  it  altogether,  though  we  may  be  able  to 
point  out  the  stopping-places  in  its  long  journey. 

I  cannot  help  thinking  that  Sir  William  Hamilton  has 
unconsciously  glided  into  a  Fallacy  of  this  sort  in  his  criti- 
cism of  Dr.  Reid's  definition  of  memory.  E,eid  says, 
"  Memory  is  an  immediate  knowledge  of  things  past "  ; 
meaning  thereby,  as  it  seems  to  me,  a  present  knowledge 
of  the  past.  This,  at  any  rate,  is  a  very  common  use  of 
the  word  ;  an  action  is  said  to  be  immediate  which  takes 
place  now,  at  once,  or  without  delay.  But  immediate  is 
also  the  opposite  of  mediate  or  vicarious;  we  are  said  to 
have  an  immediate  knowledge  of  a  thing  when  we  know  it 
directly  or  in  itself,  in  contradistinction  from  knowing  it 
vicariously,  or  through  the  medium  of  an  image  or  repre- 
sentation of  itself.     In  this  sense,  Hamilton  argues  very 


OF  FALLACIES.  277 

properly  that  an  immediate  knowledge  of  the  past  is  impos- 
sible ;  and  Reid,  I  think,  would  have  agreed  with  him  ; 
while  Hamilton  would  not  have  denied  that  memory  is 
present  knowledge,  or  knowledge  which  exists  at  the  present 
time. 

Another  source  of  ambiguity,  which  is  well  exposed  by 
Whately,  is  the  supposition  that  paronymous  or  conjugate 
words  —  as  the  substantive,  verb,  adjective,  and  adverb 
formed  from  the  same  root  —  necessarily  agree  in  mean- 
ing ;  whereas,  they  often  depart  widely  from  each  other  in 
signification.  Thus,  what  is  imaginary  is  unreal ;  but  an 
image,  as  formed  from  wood  or  stone,  is  a  reality.  To  ap- 
prehend is  to  lay  hold  of,  or  to  come  to  a  knowledge  of; 
while  apprehension  often  signifies  fear,  dread. 

What  Aristotle  calls  the  Fallacy  of  Accent  (he  should 
have  explained  it  as  an  ambiguity  which  may  be  resolved 
by  accent)  may  be  illustrated  by  the  difference  between 
gallant  and  gallant ;  the  former  means  brave,  high-spirited; 
the  latter,  courteous  or  devoted  to  women.  It  is  more  diffi- 
cult to  resolve  by  accent  the  curious  ambiguity  of  the 
phrase,  not  the  least,  where  the  two  meanings  are  opposites 
of  each  other.  Thus,  "not  the  least  difference"  may 
mean  either  "  no  difference  at  all,"  or,  "  a  very  consider- 
able, perhaps  the  greatest,  difference."  In  the  former 
case,  the  phrase  is  elliptical,  standing  for  "  not  any,  not 
even  the  least,  difference."  The  least  is  excluded  or  nega- 
tived, as  in  the  phrase  "not  the  least,"  both  by  nothing 
and  by  the  greatest. 

As  De  Morgan  remarks,  "  a  statement  of  what  was  said, 
with  the  suppression  of  such  tone  as  was  meant  to  accom- 
pany it,  is  the  fallacia  accentus.  Gesture  and  manner  often 
make  the  difference  between  irony  or  sarcasm  and  ordi- 
nary assertion.  A  person  who  quotes  another,  omitting 
anything  which  serves  to  show  the  animus  of  the  meaning; 
or  me  who  without  notice  puts  any  word  of  the  author  he 

C 


278  OF   FALLACIES. 

cites  in  Italics,  so  as  to  alter  its  emphasis ;  or  one  who 
attempts  to  heighten  his  own  assertions,  so  as  to  make 
them  imply  more  than  he  would  openly  say,  by  Italics,  or 
notes  of  exclamation,  or  otherwise,  is  guilty  of  the  fallacia 
accentus." 

2.  The  Fallacy  of  Undistributed  Middle  does  not  occur 
so  frequently,  and  is  not  so  insidious,  as  that  of  Ambiguous 
Middle.  We  may  fall  into  it  unawares  by  overlooking 
the  difference  between  the  Collective  meaning  of  the  word 
<?//="  all  taken  together,"  and  its  Distributive  meaning, 
in  which  all  signifies  "  each  and  every."  Thus,  all  the 
Senators  (taken  collectively)  try  impeachments ;  all  the 
Senators  (i.  e.  each  and  every  Senator)  are  chosen  by  the 
State  legislatures. 

All  these  exercises  will  fatigue  me ; 
This  performance  is  one  of  them  ; 
Therefore,  this  performance  will  fatigue  me. 

Another  ambiguity,  which  may  serve  to  cloak  this  logical 
fault,  is  passing  from  the  Composite  to  the  Divisive,  or  from 
the  Divisive  to  the  Composite,  meaning  of  a  proposition. 
If  we  take  together  those  members  of  the  sentence  which 
ought  to  have  been  taken  separately,  it  is  called  the  soph- 
ism of  Composition ;  if  we  take  separately  what  is  true  of 
all  only  when  they  are  united,  it  is  the  sophism  of  Division. 
A  ludicrous  instance  of  the  latter  is  found  in  most  of  the 
old  text-books  on  Logic. 

Two  and  three  (taken  compositely)  are  five  ; 

Two  and  three  (taken  divisively)  are  odd  and  even  ; 

Therefore,  five  is  odd  and  even. 

An  instance  of  the  former  is  what  may  be  called  the 
Spendthrift's  Fallacy. 

All  of  these  contemplated  expenditures  (taken  separately)  are 

of  trifling  amount ; 
Therefore  all  of  them  may  be  incurred  (together)  without  ruin- 

in£  me. 


OF  FALLACIES.  279 

The  lazy  person  reasons  in  the  same  manner,  in  respect 
to  the  waste  of  an  hour  or  two  of  time,  or  to  missing  this 
or  that  favorable  opportunity.  It  behooves  such  persons 
to  remember,  that  the  predesignation  any  one  is  not  the 
equivalent  of  all  taken  collectively. 

This  is  the  nature  of  the  famous  old  Fallacy  called 
o-6)/)o?,  a  heap,  whence  the  name  Sorites  applied  to  a  differ- 
ent and  legitimate  argument.  Does  one  grain  of  corn 
make  a  heap?  No.  Do  two  grains  make  a  heap?  No. 
Do  three  grains  ?  No.  And  in  like  manner,  we  may  ask 
a  series  of  questions,  successively  adding  unity  to  the  num- 
ber, till  the  respondent  is  at  last  obliged  to  contradict  him- 
self, and  confess  what  he  has  just  denied,  that  a  single 
grain  of  corn  makes  the  only  difference  between  what  is 
not,  and  what  is,  a  heap.  The  same  sophism  was  denom- 
inated by  the  old  logicians  the  Calvus,  because  illustrated 
by  a  series  of  questions  beginning  with  the  inquiry,  whether 
pulling  one  hair  out  of  a  man's  head  made  him  bald. 
Horace  used  it  to  ridicule  the  fashion  of  valuing  ancient 
authors  simply  on  account  of  the  antiquity  of  their  pro- 
ductions. 

"  Iste  quidem  veteres  inter  ponetur  honeste, 
Qui  vel  mente  brevi  vel  toto  est  junior  anno, 
Utor  perraisso,  caudaeque  pilos  ut  equinaa 
Faulatim  vello,  et  demo  unum,  demo  etiam  unum, 
Dum  cadat  elusus  ratione  ruer  tis  acervi, 
Qui  redit  ad  fastos,  et  virtuter-i  aestimat  annis, 
Miraturque  nihil  nisi  quod  Libitina  sacravit." 

But  while  laughing  at  an  old  sophism,  we  may  be  found 
ridiculing  a  modern  paralogism.  I  have  recently  heard 
this  very  argument  gravely  reproduced  in  a  learned  Acad- 
emy, during  a  debate  on  an  important  question  of  science. 
The  answer  to  it  is  obvious ,  —  not  one  alone,  but  one  added 
to  the  previous  999,  constitutes  a  heap. 

The  Fallacy  of  the  Composite  and  Divisive  sense  is  apt 
to  be  repeated  by  the  incautious  in  estimating  the  proba- 


280  OF   FALLACIES. 

bility  of  two  events  happening  conjointly.  Though  eacn 
of  them,  taken  separately,  is  more  likely  than  not  to 
happen,  the  probability  of  their  occurrence  together  is 
of  a  very  inferior  character.  Thus,  the  probability  of  the 
first  being  represented  by  £,  and  that  of  the  second  by  |, 
that  of  their  joint  occurrence  is  the  product  of  these  two 
fractions,  or  £S,  or  much  less  than  i,  which  represents 
an  even  chance.  So  we  are  often  misled  by  the  use  of 
the  word  tendency.  We  rightly  say  that  a  given  result 
tends  to  happen  only  when  there  is  more  than  an  even 
chance  of  its  occurrence  ;  if  there  is  less  than  an  even 
chance,  it  tends  not  to  happen.  This  is  the  form  of  a  com- 
mon blunder  in  the  doctrine  of  means  or  averages.  Thus, 
all  persons  who  have  attained  the  age  of  twenty-four  sur- 
vive on  an  average  till  they  are  sixty-two  years  old.  But 
no  one  person,  now  aged  twenty-four,  has  a  right  to  expect 
that  this  average  will  be  exemplified  in  his  particular  case. 
On  the  contrary,  his  chance  of  attaining  the  precise  age  of 
sixty-two,  no  more  and  no  less,  is  very  much  less  than  his 
chance  of  dying  at  some  other  age.  All  (collectively)  tend 
to  the  average ;  but  no  one  tends  to  the  average.  This  is 
no  paradox;  for  the  average  is  only  a  compensation  of 
errors,  and  therefore  remains  the  same  whether  the  errors 
are  great  or  small,  provided  only  that  they  are  equally  dis- 
tributed on  all  sides  of  the  average;  and  such  equality  of 
distribution  is  the  direct  consequence  of  the  fact,  that  no 
one  error  has  any  tendency  to  be  on  one  side  of  the  average 
rather  than  on  any  other  side.  No  one  tends  to  the  aver- 
age, but  tends  equally,  or  indifferently,  to  depart  from  it. 

Mr.  Darwin,  in  his  theory  of  "  the  Origin  of  Species  by 
Natural  Selection,"  is  guilty  of  both  of  these  forms  of  the 
Fallacy.  He  first  argues,  that  the  specific  Marks  of  Spe- 
cies, both  in  the  animal  and  vegetable  kingdoms,  tend  to 
vary,  because,  perhaps  in  one  case  out  of  ten  thousand,  a 
child  is  born  with  six  fingers  on  one  hand,  or  a  cat  with 


OF  FALLACIES.  281 

blue  eyes,  or  a  flo\i  er  grows  out  of  the  middle  of  another 
flower.  Collecting  many  instances  of  such  sports  of  nature 
or  monstrosities,  he  bases  his  whole  theory  upon  them,  for- 
getting that  the  vastly  larger  number  of  normal  growths 
and  developments  proves  that  the  tendency  is  to  non-varia- 
tion. Then,  secondly,  because  perhaps  one  out  of  a  hun- 
dred of  these  abnormal  Marks  is  transmitted  by  inheritance, 
he  assumes  that  these  freaks  of  nature  tend  to  perpetuate 
themselves  in  a  distinct  race,  and  thus  to  become  perma- 
nent Marks  of  distinct  species.  Thirdly,  as  either  of  the  two 
preceding  points,  taken  singly,  affords  no  basis  whatever 
for  his  doctrine,  he  assumes  that  their  joint  occurrence 
is  probable,  because  he  has  made  out  what  is,  in  truth,  a 
very  faint  probability  that  each  may  separately  happen. 
But  if  the  chance  of  a  variation  in  the  first  instance  is  only 
one  out  of  a  thousand,  and  that  of  the  anomaly  being 
handed  down  by  descent  is  one  out  of  a  hundred,  the 
probability  of  a  variation  established,  by  inheritance  is  but 
one  out  of  a  hundred  thousand.  As  the  theory  further 
requires  the  cumulation  of  an  indefinite  number  of  such 
variations  one  upon  another,  the  formation  of  a  new  species 
by  the  Darwinian  process  may  be  safely  pronounced  to  be 
incredible. 

3.  The  third  class  of  Fallacies,  those  which  arise  from  a 
violation  of  the  Rule  that  neither  Term  must  be  distributed 
in  the  Conclusion  if  it  was  not  distributed  in  the  Premise, 
are  frequent  enough,  but  will  deceive  no  one  if  they  are 
not  ambiguously  expressed.  If  it  is  the  Predicate  of  the 
Conclusion  which  is  illogically  distributed,  the  error  is 
called  an  Illicit  Process  of  the  Major  Term ;  if  the  Sub- 
ject, an  Illicit  Process  of  the  Minor  Term.  Of  these,  the 
former  is  more  common  and  insidious  ;  for  as  the  Quantity 
of  the  Predicate  is  not  expressed  in  the  ordinary  use  of 
language,  we  are  apt  to  forget  that,  in  a  Negative  propo- 
sition, it  is  always  presumed  to  be  Universal,  and  in  an 


282  OF   FALLACIES. 

Affirmative,  if  nothing  be  said  to  the  contrary,  it  is  usually 
Particular.  In  what  the  Aristotelians  call  Indefinite  prop- 
ositions, the  Quantity  of  neither  Term  is  expressed  ;  but  if 
Affirmative,  both  Terms  are  commonly  understood  to  be 
distributed ;  for  most  propositions  of  this  sort  are  either 
Definitions,  or  statements  of  a  general  law ;  and  in  both  of 
these  cases,  the  Universal  quantification  of  each  Term  is 
easily  supplied  in  thought.  Thus,  Falsehood  is  wilful  decep- 
tion, is  easily  and  properly  construed  to  mean,  All  falsehoods 
are  all  wilful  deceptions  ;  and  Matter  gravitates,  to  mean,  All 
matter  is  all  that  gravitates*  But  statements  of  a  general 
law  must  be  carefully  distinguished  from  statements  of  the 
application  of  such  a  law  to  a  particular  class  of  cases ; 
thus,  Stones  gravitate,  means  only,  "All  stones  are  some 
gravitating  substances." 

All  birds  are  winged ; 
The  bat  is  not  a  bird ; 
Then  the  bat  is  not  winged. 
Here,  the  Conclusion  is  logically  false,  for  it  contains  an 
Illicit  Process  of  the  Major  Term.     The  Sumption  is  un- 
derstood to  mean  only  that  "All  birds  are  some  winged 
things " ;   the  bat,  therefore,   though  not  a  bird,  may  be 
(as  here  it  happens  actually  to  be)  one  of  the  other  some 
winged  things,  while  the  illogical  Conclusion  declares  it  to 
be  not  Qamf)  winged  thing. 

No  slave  has  his  rights  ; 

All  slaves  are  persons  of  African  descent ; 

Therefore  no  person  of  African  descent  has  his  rights. 
The  Illicit  Process  is  here  of  the  Minor  Term  ;  for  the 
Conclusion  denies  of  any,  what  the  Premises  authorize  us 
to  deny  only  of  some  Africans. 

In  both  these  cases,  the  Fallacy  is  so  obvious  that  it  can- 
not deceive  any  one  who  thinks  clearly.  But  the  ambigui- 
ties of  language  may  so  cloak  the  deception  as  to  render 
its  exposure  difficult.     Most  insidious  in  this  respect  •  is  the 


OF  FALLACIES.  288 

ambiguity  betweon  what  is  true  absolutely^  and  what  is 
true  only  in  some  respect,  to  dirXcos  rj  firj  a7r\<w?.  From 
this  confusion  of  language  two  modes  of  false  reasoning 
result,  the  first  of  which  is  denominated  by  the  Aristo- 
telians the  fallacia  a  dicta  secundum  quid  ad  dictum  sim- 
pliciter.  It  consists  in  inferring  something  as  true  of  .the 
subject  simply,  or  without  limitation,  which  is  true  of  it  only 
in  some  respect.  Thus,  Man  is  immortal  (in  respect  to  his 
soul)  ;  therefore,  man  is  immortal  (absolutely,  both  as  to 
soul  and  body).  The  second  has  been  called  the  fallacia 
accidentis,  because  it  confounds  an  accidental  attribute  with 
what  is  essential  or  principally  intended.  But  as  it  is  the 
exact  converse  of  the  former,  it  should  rather  be  called  the 
fallacia  a  dicto  simpliciter  ad  dictum  secundum  quid.  Thus, 
to  take  the  converse  of  the  former  instance,  Man  is  mortal 
(man  being  here  understood,  as  usual,  to  be  a  living  or- 
ganism) ;  therefore,  man  is  mortal  (as  respects  his  soul). 
Aristotle  gives  the  following  illustration,  which  is  puerile, 
though  it  might  well  puzzle  a  beginner :  — 
Socrates  is  not  Coriscus  (in  any  sense)  ; 
But  Coriscus  is  a  man  (this  being  one  of  his  characteristics)  ; 
Therefore,  Socrates  is  not  a  man. 

The  most  difficult  cases  to  be  resolved  are  those  in 
which  giving  the  name  of  the  genus,  to  which  the  subject 
belongs,  is  confounded  with  giving  the  name  of  its  species. 
Thus, 

He  who  calls  you  a  man  speaks  truly ; 

He  who  calls  you  a  knave  calls  you  a  man ; 

Then  he  who  calls  you  a  knave  speaks  truly. 
A  ludicrous  instance  of  the.  former  mode  of  the  Fallacy  is 
found  in  most  of  the  text-books  :  — 

What  you  bought  yesterday  you  eat  to-day  ; 

But  you  bought  raw  meat  yesterday ; 

Then  you  eat  raw  meat  to-day.' 
Perhaps  both  forms  of  this  Fallacy  are  best  resolved  bv 


234  OF   FALLACIES. 

considering  that  the  ambiguity  resides  in  the  Copula, 
When  one  tiling  is  predicated  of  another,  it  is  seldom  un- 
derstood that  the  Predicate  is  thereby  entirely  identified 
with  the  Subject,  as  the  proposition  would  then  be  merely 
tautologous,  A  is  A.  But  unless  it  is  so  identified,  we  can- 
not affirm  of  the  Predicate  all  that  might  be  affirmed  of  the 
Subject.  The  logical  rule  as  usually  enounced,  that  no 
Term  must  be  distributed  in  the  Conclusion  if  it  was  not 
distributed  in  the  Premises,  is  defective  ;  for  it  only  insures 
that  the  Quantity  shall  be  the  same.  The  sense  ought  also 
to  be  the  same  throughout,  whether  absolute  or  relative, 
whether  in  one  respect  or  in  many,  whether  essentially  or 
accidentally.  An  adequate  enouncement  of  the  rule  would 
be,  that  no  more  arid  no  less,  in  any  respect,  must  be  collected 
in  the  Conclusion  than  was  given  out  in  the  Premises.  In 
order  to  know  how  much  was  so  given  out,  we  must  consider 
the  meaning  of  the  Copula,  is,  in  each  separate  case.  Mr. 
De  Morgan  says :  "  The  most  common  uses  of  the  verb 
are,  —  1.  absolute  identity,  as  in  'the  thing  he  sold  you 
is  the  one  I  sold  him,' — this  is  the  dictum  simpliciter ; 
2.  agreement  in  a  certain  particular  or  particulars  under- 
stood," dictum  secundum  quid,  "  as  in  '  he  is  a  negro,'  said 
of  a  European  in  reference  to  his  color ;  3.  possession  of  a 
quality,  as  in  4  the  rose  is  red ' ;  4.  reference  of  a  species  to 
its  genus,  as  in  '  man  is  an  animal.'  All  these  uses  are 
independent  of  the  use  of  the  verb  alone,  denoting  exist- 
ence, as  in  '  man  is  [i.  e.  exists].'  "  In  most  cases,  these 
meanings  are  not  interchangeable  ;  and  whenever  they  are 
not,  a  Fallacy  may  be  founded  upon  the  difference  between 
any  two  of  them. 

But  the  enumeration  is  imperfect ;  several  additions  may 
be  made  to  it,  by  observing,  what  has  been  already  re- 
marked in  treating  of  Contradiction,  "  that  two  Judgments 
properly  contradict  each  other  only  when  that  which  is 
affirmed   by  the  one  is  denied  by  the  other,  —  1.  in  the 


OF  FALLACIES.  285 

same  respect ;  2.  in  the  same  manner ;  3.  in  the  same 
degree ;  4.  at  the  same  time."  Tims,  Mr.  De  Morgan's 
instance  of  absolute  identity  is  unhappily  chosen  ;  for  if  the 
limitation  of  time  is  taken  into  account,  "  the  horse  winch 
he  sold  you,"  being  ten  years  old,  is  not  absolutely  the  same 
horse  which  I  sold  him,  as  that  was  only  six  years  old. 
All  Fallacies  of  this  class  may  be  easily  resolved  by  merely 
completing  in  expression  what  was  previously  only  implied 
in  thought.  We  thereby  prevent  any  more  or  less  stress 
being  laid  upon  an  accident,  or  upon  any  view  of  the  sub- 
ject, in  the  Conclusion,  than  was  done  in  the  Premises. 

The  use  of  wine  is  destructive  to  the  health  ; 

Therefore  its  use  ought  to  be  forbidden. 

As  stated,  this  Enthymeme  may  seem  indisputable ;  but 
there  can  be  no  practical  application  of  it,  unless  it  is  under- 
stood to  mean  that  any  use  of  wine  is  pernicious,  and  hence 
that  it  ought  always  to  be  forbidden.  This  is  the  fallacy 
of  arguing  against  the  use  of  a  thing  merely  from  its  liabil- 
ity to  abuse.  The  proper  caution  is,  that  no  change  what- 
ever in  the  Terms  employed  must  take  place  during  the 
process  of  inference. 

In  ordinary  language,  few  terms  are  so  loosely  used,  or 
so  often  improperly  applied,  as  the  same,  all,  always,  &c. 
Hence  the  logicians  were  obliged  to  form  a  separate  class 
of  Fallacies,  which  they  called  those  fictce  universalitatis. 
People  say  the  same,  when  they  mean  similar ;  all,  when 
they  mean  only  most;  and  always  signifies  to  them  the 
same  as  frequently.  They  do  not  even  mention  the  excuse 
which  the  Psalmist  alleges  when  conscious  of  his  exaggera- 
tion, —  "  I  said  in  my  haste,  All  men  are  liars."  It  was 
once  considered  a  difficult  question,  whether  a  stocking, 
which  had  been  so  much  darned  that  not  a  thread  of  the 
original  fabric  remained,  was,  or  was  not,  the  same  stocking. 
But  it  can  present  no  difficulty  to  one  who  considers  that 
samen  "ss  or  identity  is  an  absolute  term,  which  can  neither 


286  OF   FALLACIES. 

be  affirmed  nor  denied  except  in  an  unqualified  sense ;  and 
that  all  which  can  be  truly  predicated  of  what  comes  short 
of  sameness  is  similarity, 

"  We  might  suppose  that  most  persons  have  no  idea  cf  a 
universal  proposition ;  but  use  the  language,  never  intend- 
ing all  to  mean  more  than  most.  And  in  the  same  manner, 
principles  are  stated  broadly  and  generally,  which  the 
assertor  is  afterwards  at  liberty  to  deny,  under  the  phrase 
that  he  does  not  carry  them  so  far  as  the  instance  named. 
It  would  not  do  to  avow  that  the  principle  is  not  always 
true  ;  so  it  is  stated  to  be  always  true,  but  not  capable  of 
being  carried  more  than  a  certain  length.  Are  not  many 
persons  under  some  confusion  about  the  meaning  of  the 
word  general?  In  science,  it  always  has  the  meaning  of 
universal;  and  the  same  in  old  English.  Thus  the  Cate- 
chism of  the  Church  of  England  asserts  that  there  are  two 
sacraments  which  are  generally  [universally]  necessary  to 
salvation, — meaning,  necessary  for  all  of  the  genus  in  ques- 
tion, be  it  man,  Christian,  member  of  the  Church,  or  any 
other.  But  in  modern  and  vernacular  English,  general 
means  only  usual,  and  generally  means  usually."  * 

An  opposite  error,  but  one  proceeding  from  the  same 
source,  viz.  from  confounding  the  Universal  with  the  Par- 
ticular, is  committed  by  many  Americans  and  some  Eng- 
lishmen in  respect  to  the  word  quite.  Its  proper  meaning 
is  completely,  entirely,  as  "  quite  contrary  principles  "  ;  but 
it  is  often  used  in  the  sense  of  very,  as  "  quite  warm,'" 
"  quite  cold,"  "  quite  recent." 

The  word  same,  in  ordinary  parlance,  is  applied  to  all 
objects  for  which  a  single  description  will  serve,  or  which 
are  included  under  one  Concept.  Thus  we  say,  "  This 
writing  is  on  the  same  paper  with  that,"  meaning  the 
same  kind  of  paper ;  "  This  erroneous  reasoning  is  the  same 
Fallacy  with  the  other,"  meaning  the  same  kind  of  Fallacy. 

*  De  Morgan's  Formal  Logic,  p.  272. 


OF   FALLACIES.  287 

A  description  or  Concept,  as  we  have  seen,  is  an  imperfect 
enumeration  of  the  qualities  of  a  whole  class  of  objects ; 
and  it  is  only  because  the  enumeration  is  imperfect  that 
many  can  be  ranked  under  one  class.  A  perfect  enumera- 
tion, if  such  were  possible,  —  a  list  of  all  the  qualities,  — 
would  cause  each  Individual  (if  this  were  not  a  contradic- 
tion in  terms)  to  constitute  a  class  by  itself. 

"  Nothing,  perhaps,"  says  Dr.  Whately,  "  has  contributed 
more  to  the  error  of  Realism,  than  inattention  to  this  ambi- 
guity. When  several  persons  are  said  to  have  one  and  the 
same  opinion,  thought,  or  idea,  many  men,  overlooking  the 
true,  simple  statement  of  the  case,  which  is,  that  they  are 
all  thinking  alike  [or  similarly],  look  for  something  more 
abstruse  and  mystical,  and  imagine  there  must  be  some  one 
thing,  in  the  primary  sense,  though  not  an  Individual, 
which  is  present  at  once  in  the  mind  of  each  of  these  per- 
sons; and  thence  readily  sprung  Plato's  theory  of  Ideas, 
each  of  which  was,  according  to  him,  one  real,  eternal 
object,  existing  entire  and  complete  in  each  of  the  Indi- 
vidual objects  that  are  known  by  one  name.*  Hence,  first 
in  poetical  mythology,  and  ultimately,  perhaps,  in  popular 
belief,  Fortune,  Liberty,  Prudence  (Minerva),  a  Boundary 
(Terminus),  and  even  the  Mildew  of  Corn  (Rubigo),  be- 
came personified,  deified,  and  represented  by  statues ; 
somewhat  according  to  the  process  which  is  described  by 
Swift,  in  his  humorous  manner,  in  speaking  of  Zeal,  in  the 
4  Tale  of  a  Tub,'  '  how  from  a  notion  it  became  a  word, 
and  thence,  in  a  hot  summer,  ripened  into  a  tangible  sub- 
stance.' " 

But  Dr.  Whately  seems  to  depart  from  his  own  prin- 

*  "  When  abstract  truth  is  contemplated,"  asks  Dr.  Price,  "  is  not  the 
very  object  itself  present  to  the  mind  ?  When  millions  of  intellects  contem- 
plate the  equality  of  every  angle  in  a  semicircle  to  a  right  angle,  have  they 
not  all  tite  same  object  in  view  1  Is  this  object  nothing  ?  Or  is  it  only  an 
image  or  kind  of  shadow  1     These  inquiries  carry  our  thoughts  high." 


288  OF  FALLACIES. 

ciples,  when  he  proceeds  to  remark,  that  "  Sameness,  in 
the  primary  sense,  does  not  even  necessarily  imply  Simi- 
larity ;  for  if  we  say  of  any  man  that  he  is  greatly  altered 
since  such  a  time,  we  understand,  and  indeed  imply  by 
the  very  expression,  that  he  is  one  person,  though  different 
in  several  qualities;  else  it  would  not  be  Ae."  Surely, 
what  we  mean  by  Personal  Identity  is  sameness  of  sub- 
stance under  great  differences  of  phenomenal  manifestation. 
Sameness  here  does  not  imply  Similarity,  merely  because 
it  implies  a  great  deal  more ;  —  namely,  absolute  oneness 
of  substance,  under  the  greatest  diversity  of  outward  ap- 
pearance. The  Person  is  not  different  at  different  times, 
but  his  attributes  and  actions  are.  But  perhaps  this  is 
what  Dr.  Whately  really  means,  though  it  is  not  the  ob- 
vious construction  of  his  language.  He  seems  to  consider 
the  Person,  and  his  outward  character  or  manifestation,  as 
one. 

The  Fallacy  of  over-hasty  generalization  is  very  frequent, 
as  Bentham  remarks,  in  political  reasoning.  It  consists  in 
attributing  to  an  individual  person  or  thing  certain  attri- 
butes which  appear  in  many  or  most  others  which  have 
been  loosely  ranked  in  the  same  class  with  the  object  in 
question,  and  thereby  designated  by  the  same  name.  Thus, 
a  pamphlet  entitled  "  The  Crimes  of  Kings"  was  published 
in  Paris  in  1792,  in  order  to  prove  that  Louis  XVI.  ought 
to  be  put  to  death.  In  like  manner,  "  The  Cruelties  of 
Catholics  "  was  the  title  of  a  book  published  in  England  as 
an  argument  against  Catholic  Emancipation.  Most  polit- 
ical harangues  abound  in  arguments  of  the  like  character ; 
but  they  are  evidently  addressed  to  the  passions  rather 
than  the  intellect,  as  they  cannot  deceive  any  one  who  is 
cool  enough  to  be  able  to  think. 

To  the  ambiguity  between  what  is  true  absolutely,  and 
what  is  true  only  in  some  respect,  may  be  referred  the 
famous  sophism  of  Eubulides,  called  WevSo/jLevos,  the  Liar. 


OF  FALLACIES.  289 

According  to  Diogenes  Laertius,  Chrysippus  the  Stoic  wrote 
six  different  treatises  upon  this  logical  puzzle,  and  Philetas 
of  Cos  studied  himself  to  death  in  the  vain  attempt  to  solve 
it.  "  If  you  say  that  you  he,  and  say  so  truly,  then  you 
do  lie  ;  but  if  you  say  so  falsely,  then  you  speak  the  truth. 
In  either  case,  therefore,  the  same  assertion  is  both  true 
and  false."  But  if  any  one  says,  "  I  lie,"  his  assertion  is 
not  a  dictum  simpliciter ;  for  a  lie  is  only  possible  secundum 
quid.  He  who  lies  must  lie  about  something,  in  some  par- 
ticular affirmation  or  denial ;  otherwise,  his  assertion  is  as 
meaningless  as  the  remark  that  "  something  is  very  like." 
Like  what  ?  *  If  he  means  only,  "  I  have  lied  in  some 
former  assertion,"  there  is  no  contradiction ;  if  he  means, 
"I  lie  now,  in  saying  that  4I  lie,' "  he  really  makes  two 
affirmations,  of  which  the  one,  the  oratio  obliqua^  is  vague 
and  meaningless,  and  the  other,  the  oratio  directa,  improp- 
erly characterizes  this  one  as  a  falsehood,  —  improperly,  for 
that  which  has  no  significance  cannot  be  either  true  or 
false. 

This  sophism  has  been  stated  in  a  different  and  inferior 
form,  as  follows  :  — 

"  All  the  Cretans  are  liars." 

But  Epimenides,  who  says  this,  is  himself  a  Cretan. 

Therefore,  as  he  is  a  liar,  this  saying  is  not  true. 

But  if  the  saying  is  not  true,  Epimenides  may  have  spoken  the 

truth. 
Then  the  saying  is  true ;  —  and  so  on,  as  before. 

But  here  the  Major  Premise  does  not  support  the  Con- 
clusion, unless  it  is  construed  to  mean  that  the  Cretans  are 
always  liars,  —  that  they  cannot  speak  the  truth.  And 
even  if  this  were  true,  one  who  is  himself  a  Cretan  could 
not  say  so,  for  then  he  would  speak  truly,  and  so  contra- 
dict himself.     Of  a  similar  nature  is  the  following  puzzle. 

*  Mansel's  Notes  to  Aldrich,  p.  145. 
13  S 


290  OF  FALLACIES. 

"  No  rule  holds  true  without  some  exceptions." 

But  this  very  remark  is  a  rule. 

Then  it  has  exceptions. 

Then  there  are  rules  without  exceptions. 

Here  the  reasoning,  as  such,  is  correct,  and  the  absurd- 
ity to  which  it  leads  demonstrates  what  has  been  properly 
called  the  Fallacy  of  universal  scepticism.  As  Sir  James 
Mackintosh  remarks,  "  universal  scepticism  involves  a  con- 
tradiction in  terms ;  it  is  a  belief  that  there  can  be  no 
belief."  He  who  denies  every  assertion  thereby  denies  his 
own  denial,  and  so  contradicts  himself.  The  Major  Pre- 
mise in  this  very  puzzle  is  such  a  self-contradictory  asser- 
tion ;  I  cannot  make  a  true  general  remark,  that  all  general 
remarks  are  false ;  or,  what  is  the  same  thing,  that  they 
"  have  exceptions." 

4  &  5.  Little  need  be  said  to  illustrate  the  remaining 
classes  of  Fallacies,  as  they  are  of  infrequent  occurrence, 
and  are  easy  to  be  detected  unless  cloaked  by  some  of  the 
ambiguities  of  language  which  have  already  been  exposed. 
Those  which  respect  the  Quality  of  the  reasoning  may  well 
be  considered  together.  The  two  Rules  are,  that  at  least 
one  of  the  Premises  must  be  Affirmative,  and  that  the  Con- 
clusion must  be  Negative  if  either  Premise  is  Negative. 
These  Rules  may  be  violated  in  appearance,  when  they  are 
not  so  in  reality.     For  instance :  — 

No  one  is  rich  who  has  not  enough ; 

No  miser  has  enough  ; 

Therefore  no  miser  is  rich. 
Here,  both  Premises  are  seemingly  negative ;  but  they 
are  not  really  so,  for  the  negation  of  having  enough  is  a 
part  of  the  Predicate,  and  therefore  does  not  affect  the 
Quality  of  the  Judgment,  which  depends  on  the  Copula. 
Instead  of  not  having  enough,  substitute  the  equivalent 
•ohrase,  wanting  more,  and  the  seeming  incorrectness  is 
amoved. 


OF  FALLACIES.  291 

No  one  who  wants  more  is  rich ; 
Every  miser  wants  more ; 
Therefore  no  miser  is  rich. 

As  has  been  shown  in  treating  of  Exponibles,  the  Ex- 
clusive proposition,  "  None  but  Whites  are  civilized,"  is 
really  complex  ;  it  contains  one  direct  assertion,  respecting 
all  non-  Whites,  that  they  are  not  civilized,  and  one  implied 
assertion,  that  some  Whites  are  civilized.  Then  the  follow- 
ing syllogism  is  valid,  though  each  of  its  three  Judgments 
appears  to  be  negative. 

None  but  Whites  are  civilized ;  =  No  non-White  is  civilized ; 
The  Hindoos  are  not  Whites  ;  =  The  Hindoos  are  non- Whites ; 
The  Hindoos  are  not  civilized. 

Two  ludicrous  instances,  which  have  often  been  repeated 
in  the  books,  are  enough  to  illustrate  the  Fallacy  which 
arises  from  a  violation  of  the  fifth  Rule,  though  both  of 
them  can  be  referred  also  to  one  of  the  other  classes  which 
have  been  already  considered. 

Nothing  is  heavier  than  platinum ; 
Feathers  are  heavier  than  nothing ; 
Therefore,  feathers  are  heavier  than  platinum. 

This  sophism  cannot  puzzle  even  a  beginner,  and  is  of 
the  same  character  in  the  following. 

No  cat  has  two  tails  ; 

Every  cat  has  one  tail  more  than  no  cat ; 

Therefore,  every  cat  has  three  tails. 

The  Fallacy  plurium  interrogationum,  as  it  was  called, 
may  be  brought  under  this  head  by  being  referred  to  the 
ambiguous  construction  of  sentences.  It  is  a  mere  trick, 
which  consists  in  asking  two  or  more  questions  as  if  they 
were  one;  then  the  respondent  is  entrapped  whether  he 
answers  in  the  Affirmative  or  the  Negative,  as  either  will 
be  inappropriate  to  one  or  the  other  of  the  two  interroga- 
tories.    Of  course,  the  Fallacy  is  solved  by  dividing  the 


292  OF   FALLACIES. 

questions  and  answering  them  separately.  The  standard 
illustration  is  asking  a  man  "  whether  he  has  ceased  beating 
his  father."  Lawyers  are  often  guilty  of  this  sophism 
while  examining  a  witness  in  court,  by  insisting  that  he 
shall  give  what  they  call  "a  categorical  answer";  —  that 
is,  that  he  shall  say  either  Yes  or  No.  But  to  the  question 
as  they  propound  it,  either  Yes  or  No  will  be  a  false 
answer.  A  question  often  involves  a  real  duplicity  under 
a  seeming  unity,  as  the  uncertainty  may  regard,  not  the 
meaning,  but  the  extension,  of  the  Terms  employed ;  and  the 
same  ambiguity  may  lurk  in  a  categorical  proposition,  or  in 
the  answer  to  an  interrogatory.  The  distinction  between 
Contraries  and  Contradictories,  and  the  relation  between 
Sub-Contraries,  must  be  kept  in  view.  He  who  denies 
that  all  are  lost,  does  not  thereby  deny  that  some,  perhaps 
many,  even  all  but  one,  have  perished.  Some  are  not  may 
mean  perhaps  all  are  not,  or  some  certainly  are.  To  assert 
or  deny  a  particular  motive  for  an  action,  is  still  to  leave  the 
question  undecided  as  to  the  concurrence  of  many  motives, 
and  to  say  nothing  about  their  comparative  strength. 
Most  of  our  actions  proceed  from  a  mixture  of  motives, 
and  the  agent  himself  may  not  be  able  to  say  which  was 
the  principal.  Men  easily  deceive  themselves  in  this 
respect,  as  their  memory,  their  vanity,  or  even  their  re- 
morse, may  mislead  them ;  and  the  mistake  is  especially 
frequent  when  conscientious  or  religious  motives  are  in 
question. 

Those  who  made  it  their  business  to  invent  logical  puz- 
zles, and  to  entrap  an  opponent  in  disputation,  often  secured 
their  Premises  beforehand,  by  requiring  their  interlocutor 
to  answer  a  series  of  questions.  Socrates  was  a  great  mas- 
ter of  this  eristic  art ;  but  though  it  may  fairly  and  profita- 
bly be  employed  in  the  communications  of  a  teacher  with 
his  pupils,  a  free  use  of  it  may  reduce  an  opponent  to  silence 
without  convincing  him.     In  Plato's   Dialogues,  Socrates 


OF  FALLACIES.  293 

often  appears  in  no  better  light  than  a  satirical  disputant 
quibbling  about  the  meaning  of  words.  The  following 
instance  of  the  Fallacy  plurium  interrogationum,  which  1 
borrow  from  Fries,  would  not  puzzle  any  one  if  it  were  not 
stated  in  the  form  of  questions  and  answers. 
Is  it  net  true  that  you  must  have  lost  that  which  you  once  had, 

but  which  you  have  no  longer  ?     Yes. 
Did  you  not  have  ten  counters  when  you  commenced  the  game  ? 

Yes. 
Have  you  ten  counters  now  ?     No. 
Then  you  have  lost  ten  counters. 

But  he  still  had  eight,  having  lost  only  two ;  to  deny 
possession  of  the  whole  is  not  necessarily  to  deny  that  you 
have  a  part.  But  if  obliged  to  answer  simply  Yes  or  No, 
the  respondent  could  not  avail  himself  of  this  distinction. 

6  &  7.  From  Dr.  Whately's  convenient  collection  of 
"  examples  for  the  exercise  of  learners,',  to  which  I  have 
been  indebted  for  several  of  the  preceding  illustrations,  I 
borrow  the  following  instances  of  violation  of  the  Canons 
of  hypothetical  reasoning. 

If  penal  laws  against  Papists  were  enforced,  they  would  be  ag- 
grieved ; 
But  they  are  not  enforced ; 
Therefore,  the  Papists  are  not  aggrieved. 

Though  this  argument  was  often  gravely  repeated  m 
Parliament,  and  elsewhere,  during  the  debates  on  Catholic 
Emancipation,  it  is,  of  course,  entirely  invalid  by  the  rules 
of  Logic  ;  for  from  denying  the  Antecedent  in  a  Hypo- 
thetical Judgment,  no  Conclusion  follows,  since  the  Conse- 
quent may  still  be  true  from  some  other  reason  than  the 
one  here  specified.  In  this  case,  though  the  penal  laws 
were  not  enforced,  the  Catholics  had  a  right  to  feel  ag- 
grieved  that  these  laws  should  be  permitted  to  remain  in 
the  statute-book,  as  this  was  an  insult  to  them  personally, 
and  to  their  faith. 


294  ■  OF  FALLACIES. 

We  ought  to  give  one  day  in  seven  to  religious  duties,  if  the 

Fourth  Commandment  is  obligatory  on  us ; 
But  we  are  bound  to  set  apart  one  day  in  seven  for  religion ; 
Therefore,  the  Fourth  Commandment  is  obligatory  on  us. 

The  Canon  here  violated  is,  that  from  affirming  the 
Consequent  no  Conclusion  can  be  drawn,  since  the  Conse- 
quent may  have  resulted  from  some  ©ther  reason  than  that 
specified  in  the  Antecedent.  A  little  attempt  is  here  made 
to  cloak  the  Fallacy,  by  inverting  the  natural  position  of 
the  Antecedent  and  the  Consequent  in  the  Major  Premise 

We  pass  now  to  a  consideration  of  those  fallacious  rea- 
sonings which  are  correct  in  Form,  since  the  Conclusion  is 
logically  drawn,  but  are  faulty  in  Matter,  either  from  some 
error  or  undue  assumption  in  the  Premises,  or  some  mis- 
take as  to  the  point  to  which  the  argumentation  ought  to 
be  directed.  An  exhaustive  classification  of  Material  Fal- 
lacies is  not  to  be  expected,  as  they  are  numerous  and 
varied  in  form,  and  derive  their  characteristics  chiefly  from 
the  particular  Matter  of  the  special  sciences  which  first 
suggested  them.  The  only  proper  classes  of  them  which 
have  been  separately  considered  by  logicians  are  those 
which,  ever  since  Aristotle's  time,  have  been  technically 
designated  as  the  petitio  principii,  the  ignoratio  elenchi,  and 
the  non-causa  pro  causa;  to  which  may  be  added  several 
miscellaneous  sophisms  of  so  puzzling  a  character  that  the 
old  logiaians  called  them  the  Inexplicables. 

1.  The  vulgar  equivalent  for  petitio  principii  is  begging 
the  question;  and  the  common  explanation  of  it  is,  that  it 
consists  in  assuming,  in  the  course  of  the  argument,  the 
very  point  wrhich  ought  to  be  proved.  Its  most  deceptive 
application  is  what  is  called  reasoning  in  a  circle,  in  which 
Premises  are  first  assumed,  and  subsequently  proved  by 
means  of  the  very  Conclusions  which  they  had  been  used 
to  establish.  This  error  is  more  difficult  of  detection  in 
proportion  as  the  circle  is  more  extended,  or  as  more  Syl- 


OF  FALLACIES.  295 

fogisms  are  employed  before  the  reasoner  comes  round  to 
the  very  point  that  he  started  from.  As  King  remarks, 
"  to  the  Circle  there  are  properly  required  two  probations, 
which  are  so  reciprocally  related  that  the  Antecedent  in 
the  one  is  proved  by  its  own  Consequent  in  the  other. 
The  proposition  A  is  true  because  the  proposition  B  is 
true ;  and  the  proposition  B  is  true  because  the  proposition 
A  is  true.  A  Circle  so  palpable  as  this  would,  indeed,  be 
committed  by  no  one.  The  vice  is  usually  concealed  by 
the  interpolation  of  intermediate  propositions,  or  by  a 
change  in  the  expression."  "Thus,"  says  Hamilton,  "Pla- 
to, in  his  Phcedo,  demonstrates  the  immortality  of  the  soul 
from  its  simplicity ;  and,  in  the  Republic,  he  demonstrates 
its  simplicity  from  its  immortality."  Theologians,  also, 
sometimes  fall  into  this  error,  by  first  proving  the  authority 
of  the  Church  from  the  testimony  of  the  Scriptures,  and 
then  seeking  to  establish  the  authenticity  of  the  Scriptures 
by  the  testimony  of  the  Church ;  and  the  Fallacy  escapes 
notice,  because  one  branch  of  it  is  found,  perhaps,  in  a 
polemic  tract  on  Church  government,  and  the  other  half  in 
a  treatise  on  the  Evidences. 

Strictly  speaking,  all  valid  reasoning  proceeds  ex  con- 
cessis.  Two  Premises  must  be  assumed,  or  taken  for 
granted ;  and  these  two,  taken  in  "conjunction,  necessarily 
involve  the  Conclusion.  Thus  much  must  be  conceded  to 
those  who  claim  that  every  Syllogism  presupposes  the  truth 
of  what  it  is  brought  forward  to  establish.  But  then  it  is 
presumed  that  there  is  no  undue  assumption ;  —  that  the 
two  Premises,  which  we  now  posit,  either  have  been  al- 
ready proved,  or  that  they  are  universally  admitted  truths, 
or  that  they  have  just  been  conceded,  pro  fiac  vice,  by  the 
opponent.  As  Mr.  Mansel  remarks,  "  the  petitio  principii  is 
a  material,  not  a  formal  Fallacy,  and  consists  in  assuming, 
in  demonstration,  a  non-axiomatic  principle  as  axiomatic, 
or  hi  dialectic  disputation,  a  non-probable  principle  as  prob-^ 


296  OF   FALLACIES. 

able."  It  consists  not  in  mere  assumption,  then,  for  that 
is  necessary,  but  in  undue  assumption.  That  branch  of  it 
■which  is  called  reasoning  in  a  circle  is,  from  the  nature  of 
the  case,  not  a  vice  which  can  be  committed  in  a  single 
Syllogism,  but  only  in  a  series  of  Syllogisms  constituting  a 
chain  of  proof.  That  which  vitiates  a  single  Syllogism  is 
reasoning  from  Premises,  one,  if  not  both,  of  which  either 
is  in  more  need  of  proof  than  the  very  proposition  which 
we  seek  to  prove  by  it,  or  it  is  that  proposition  itself 
only  veiled  in  other  words,  or  it  assumes  two  Terms  to 
be  mere  equivalents  of  each  other,  when  they  really  have 
not  the  same  meaning.  We  must  not  reason  like  the 
physician  in  Moliere,  who  accounts  for  opium  producing 
sleep  by  saying  that  it  has  a  soporific  virtue.  The  argu- 
ment that  locomotion  is  not  an  attribute  of  all  animals,  since 
sponges  cannot  change  their  place,  contains  the  undue  as- 
sumption that  sponges  are  animals.  Indeed,  the  Fallacy 
in  this  case  becomes  obvious  when  the  argument  is  expli- 
cated into  a  regular  Syllogism.  And  this  is  usually  so  in 
what  is  popularly  called  begging  the  question  ;  the  argument 
is  stated  as  an  Enthymeme,  and  the  suppressed  Premise  is 
that  which  contains  the  undue  assumption. 

A  petitio  principii  is  involved  in  every  case  of  reasoning 
which  depends  upon  an  Imperfect  Disjunction,  though  such 
cases  might  also  be  properly  referred  to  other  kinds  of 
Fallacy.  A  Disjunction  must  be  assumed  to  be  perfect,  or 
the  Dilemma  which  is  founded  upon  it  is  obviously  invalid. 
Of  this  character  is  the  famous  sophism  of  Diodorus  Cro- 
nus, which  professes  to  demonstrate  the  impossibility  of 
motion,  and  which  has  probably  occasioned  more  discus- 
sion than  any  other  logical  puzzle  on  record.  It  occupies 
a  high  place  among  those  which  were  formerly  called  the 
Inexplicables.  Dr.  Whately  seems  tacitly  to  admit  that  it 
is  insoluble;  for,  though  he  justly  criticises  an  attempted 
explanation  of  it  by  Aldrich,  he  proposes  nothing  to  take 
its  place.     The  sophism  may  be  thus  stated. 


OF  FALLACIES.  297 

If  motion  :s  possible,  a  body  must  move  either  in  the  place  where 

it  is,  or  in  a  place  where  it  is  not. 
But  a  body  cannot  move  in  the  place  where  it  is ;  and  of  course, 

it  cannot  move  where  it  is  not. 
Therefore,  motion  is  impossible. 

It  is  hazardous  to  differ  from  Mr.  Mansel  upon  any  logi- 
cal question ;  but  the  solution  of  this  sophism  which  he  has 
adopted  and  improved  seems  to  me  unsatisfactory.  He 
says,  "  The  true  solution  is,  that  the  disjunctive  premise  is 
false.  '  The  place  where  a  body  is,'  is  contradictory  of 
'  the  place  where  a  body  is  not ' ;  as  4  Englishmen  '  is  con- 
tradictory of  '  not-Englishmen  ' ;  but  *  moving  in  the  place 
where  it  is,'  is  no  more  contradictory  of  '  moving  in  the 
place  where  it  is  not,'  than  4  an  army  composed  of  English- 
men '  is  contradictory  of  •  an  army  composed  of  not-Eng- 
lishmen.' As  it  would  be  false  to  say,  *  Every  army  must 
be  composed  of  Englishmen  or  not-Englishmen,'  to  the  ex- 
clusion of  the  third  possibility  of  a  mixed  force,  so  it  is 
false  to  say,  i  Every  body  must  move  in  the  place  where 
it  is,  or  in  the  place  where  it  is  not,'  to  the  exclusion  of 
the  third  possibility  of  moving  partly  in  the  one  and  partly 
in  the  other.  This  solution  is  substantially  given  by 
Hobbes."  * 

Hobbes  even  gives  a  diagram  to  prove  that  a  body  — 
quantulumcunque  sit,  however  small  it  may  be  —  "  cannot, 
all  at  once,  so  leave  the  whole  of  its  former  place  that  a 
part  of  it  shall  not  be  in  that  portion  which  is  common  to 
the  two  places,  namely,  the  one  which  is  left  and  the  other 
which  is  reached."  But  the  difficulty  cannot  be  thus 
evaded.  A  part  of  a  body  cannot  be  in  two  places  at  once, 
any  more  than  the  whole.  For  suppose  that  which  moves 
to  be  a  mathematical  point,  as  in  the  geometer's  conception 
of  the  generation  of  a  line.  Such  a  point,  of  course,  being 
indivisible,  cannot  be  "  partly  in  the  one  and  partly  in  the 

*  Mansel's  Notes  to  Aldrich,  p.  144. 
13* 


298  OF   FALLACIES. 

other  "  place.  A  whole  cannot  move  unless  every  point  in 
it  moves  also.  Every  individual  must  be,  as  Mr.  Mansel 
acknowledges,  either  an  Englishman  or  a  not-Englishman. 
Reduce  the  army  to  a  single  soldier,  and  the  difficulty  of 
moving  him,  according  to  this  sophism,  is  still  insuperable. 

The  following  solution,  I  believe,  has  not  before  ap- 
peared in  print.  The  Major  Premise  of  the  sophism  is  not 
true  except  with  a  proviso  or  limitation,  which  is  improperly 
suppressed ;  so  that  the  Fallacy  may  properly  be  referred 
to  the  class  a  dicta  secundum  quid  ad  dictum  simpliciter. 
"  A  moving  body,  at  any  one  indivisible  moment,  must  be 
either  where  it  is,  or  where  it  is  not."  When  the  proviso 
here  italicized  is  expressed,  the  proposition  is  true,  the 
reasoning  is  sound,  and  the  conclusion  is  correct.  In  any 
one  indivisible  moment,  motion  is  impossible  ;  for  motion  re- 
quires time  as  well  as  space.  The  Axiom  of  Excluded 
Middle,  that  a  thing  must  be,  or  not  be,  in  a  certain  place, 
does  apply  to  a  body ;  but  it  does  not  apply  to  a  moving 
body,  and  this  is  what  covers  up  the  Fallacy.  For  in  order 
to  be  moving,  it  must,  at  the  second  indivisible  instant,  be 
where  it  was  not  at  the  first  instant.  Hence,  we  do  not 
violate  the  Axiom  when  we  deny  the  Major  Premise  as 
originally  stated  ;  for  "  a  moving  body  "  is  that  which  has 
been  where  it  now  is  not.  The  difference  of  tense  (time) 
makes  it  possible  for  the  same  thing  to  be  and  not  to  be. 
The  law  of  Excluded  Middle  itself,  as  we  have  seen,  is  time 
only  when  the  qualification  at  the  same  time  is  understood. 

A  solution  which  is  substantially  similar  to  the  one  here 
given  is  proposed  by  Mr.  De  Morgan.  Movement  is 
change,  and  so  requires  two  places ;  a  body  is  not  moved  in 
a  place,  but  from  one  place  to  another. 

2.  Ignoratio  elenchi  is  what  we  should  now  call  answer- 
ing to  the  wrong  point.  It  is  proving  something  which 
does  not  really  controvert  your  antagonist's  position,  though 
it  is  assumed  to  do  so.     An  Elenchus  is  a  Syllogism  which 


OF  FALLACIES.  299 

will  confute  the  argument  of  your  opponent ;  and  ignoratio 
elenchi  is  ignorance  of  what  will  so  confute  him,  —  igno- 
rance of  the  fact  that  your  Conclusion,  even  if  it  were 
established,  would  not  contradict  his  Conclusion.  This 
error  in  reasoning  is  so  common,  that  special  precautions 
have,  in  some  cases,  been  adopted  in  order  to  obviate  it. 
Thus,  in  Law,  the  only  object  of  what  is  called  special 
plea  ling  is,  to  ascertain  the  precise  point  at  issue,  or  to 
prevent  irrelevancy  of  evidence  and  argument  by  binding 
both  parties  in  the  suit  to  address  themselves  to  what  is 
really  the  sole  point  in  controversy.  A  Demurrer  has  been 
happily  explained  to  be  equivalent  to  the  remark,  "  Well, 
what  of  that?"  Even  granting  the  facts  stated  in  the 
declaration  to  be  true,  it  may  be  insisted  that  these  facts 
give  the  plaintiff  no  ground  of  action ;  and  hence,  that  it 
was  an  ignoratio  elenchi  to  state  them  at  all. 

As  the  Port  Royal  logicians  remark,  the  passions  of  men 
afford  the  reason  why  this  sophism  is  so  common  in  con- 
troversy. "  We  dispute  with  warmth,  and  often  without 
understanding  one  another.  Passion  or  bad  faith  leads  us 
to  attribute  to  our  adversary  that  which  is  very  far  from 
his  meaning,  in  order  to  carry  on  the  contest  with  greater 
advantage;  or  to  impute  to  him  consequences  which  we 
imagine  may  be  derived  from  his  doctrine,  although  he 
disavows  and  denies  them.  All  this  may  be  reduced  to 
this  kind  of  sophism,  which  an  honest  and  good  man  ought 
to  avoid  above  all  things." 

1  Logicians  have  distinguished  and  described  certain  kinds 
of  argument  which  are  valid,  and  may  fairly  enough  be 
used,  provided  that  it  is  clearly  seen  and  admitted  that  they 
have  no  bearing  upon  the  main  question.  The  Fallacy 
consists  in  referring  such  arguments  to  a  wrong  Conclusion, 
in  urging  them  as  if  they  established  the  real  point  of  con- 
troversy, whereas  they  actually  tend  only  to  direct  censure 
or  laughter  against  those  who  hold  the  opposite  opinion,  or 


800  OF  FALLACIES. 

to  some  other  equally  irrelevant  object.  Let  the  reasoning 
which  tends  directly  to  prove  the  main  point  at  issue  be 
called  the  argumentum  ad  rem.  Then  the  argumentum  ad 
hominem  is  that  which  convicts  your  opponent  of  inconsis- 
tency, ignorance,  bad  faith,  or  illogical  reasoning.  Any  or 
all  these  charges  may  be  well  founded,  but  they  are  aside 
from  the  purpose ;  for  the  doctrine  which  is  in  dispute  may 
be  well  founded,  though  its  supporter  is  deficient  in  all  the 
qualities  of  a  good  reasoner.  The  argumentum  ad  vere- 
cundiam  appeals  to  our  reverence  for  some  high  authority, 
or  some  venerable  institution,  as  a  means  of  silencing  an 
opponent,  but  not  of  convincing  him  that  he  is  mistaken 
in  opinion.  The  argumentum  ad  populum  is  a  similar 
appeal  to  the  passions  or  prejudices  of  common  people  ;  it 
is  a  fair  inference  that  proper  arguments  are  wanting,  when 
such  appeals  are  permitted. 

To  these  must  be  added  the  argumentum  ad  ignorantiam, 
which  is  asserting  that  your  own  position  is  correct,  unless 
your  opponent  can  show  some  valid  reason  to  the  con- 
trary. This  mistake  is  often  committed  with  reference  to 
alleged  occurrences  which  appear  to  us  strange  and  improb- 
able, or  which  we  may  even  believe  to  be  impossible.  The 
Fallacy  consists  in  denying  that  the  thing  is  so,  merely  be- 
cause we  do  not  know  how  it  is  so.  But  if  this  reasoning 
were  correct,  we  ought  to  deny  that  the  human  will  has 
any  control  over  a  single  movement  of  our  animal  organ- 
ism, or  even  that  the  grass  grows ;  for,  certainly,  no  one 
can  tell  how  a  mere  volition  moves  the  arm,  or  how  the 
green  herb  in  the  spring-time  absorbs  inorganic  matter  and 
assimilates  it  to  itself.  But  our  ignorance  of  one  thing,  the 
modus  operandi,  is  no  disproof  of  a  very  different  thing,  the 
opus  operatum.  The  king  of  Siam  was  illogical  in  denying 
that  water  could  become  ice,  merely  because,  within  his 
experience,  a  liquid  had  never  become  solid.  The  incon- 
ce;^  able  is  no  sure  indication  of  the  impossible.     Sir  Wil- 


OF  FALLACIES.  301 

liam  Hamilton  even  undertakes  to  show,  that  all  which  is 
conceivable  in  thought  lies  between  two  extremes,  both  of 
which  are  inconceivable,  but  of  which,  as  they  are  contra- 
dictories of  each  other,  one  must  be  true. 

But  lest  this  exposition  should  seem  to  favor  credulity 
and  superstition,  it  should  be  observed,  that  the  paralogism 
here  exposed  is  usually  met  by  a  counter  argument  just  as 
untenable  as  the  one  which  it  is  brought  forward  to  con- 
fute. Because  neither  I  nor  you  know  how  a  certain 
phenomenon  is  produced,  I  am  not  justified  in  arbitrarily 
assigning  it  to  a  certain  cause,  whether  natural  or  super- 
natural, and  then  calling  upon  you  to  accept  this  explana- 
tion for  want  of  a  better.  This  also  would  be  an  appeal 
to  ignorance,  —  an  attempt  to  found  knowledge  upon  ig- 
norance. To  take  an  instance  from  the  reputed  wonders 
of  animal  magnetism ;  —  perhaps  I  do  not  know  how  the 
table  tips ;  but  you  are  not  therefore  to  assume  that  spirits 
from  the  other  world  are  tipping  it.  It  is  an  ignoratio 
elenchi  to  argue,  that  your  hypothesis  must  be  well  founded 
because  I  am  not  able  to  invent  a  better.  Your  business 
is  to  support  your  own  Conclusion  by  valid  reasoning,  not 
to  rest  it  merely  on  my  inability  to  prove  the  opposite. 

This  Fallacy  pervades  all  the  speculations  of  those  whom 
Dr.  Whewell  calls  the  uniformitarian  school  of  geologists. 
They  argue  that  the  geological  phenomena  now  visible, 
many  of  which  are  of  stupendous  magnitude,  can  be  ac- 
counted for  by  the  ordinary  working  of  physical  causes 
now  in  operation,  if  we  only  assign  a  sufficient  lapse  of  time 
for  the  cumulation  of  their  results.  It  is  unnecessary,  they 
say,  to  suppose  that  there  was  any  cataclasm,  any  violent 
disruption  of  what  is  the  usual  course  of  nature  in  our  own 
days,  in  order  to  account  for  the  elevation  of  vast  mountain 
chains,  the  sinking  of  continents,  or  the  dislocation  of  strata 
many  miles  in  thickness ;  the  same  causes,  which  are  now 
altering  the  level  of  a  continent  at  the  rate  of  an  inch  in  a 


302  OF  FALLACIES. 

century,  can  have  piled  up  the  Andes  or  the  Himalayas,  if 
you  give  them  time  enough.  Perhaps  so ;  and  yet  it  may 
be  questioned  which  is  the  more  violent  supposition,  the 
sudden  and  irresistible  outbreak  of  a  power  whose  opera- 
tions, at  least  on  so  grand  a  scale,  have  never  since  been 
witnessed,  or  the  undisturbed  lapse  of  those  countless  mil- 
lions of  ages  on  which  the  imaginations  of  geologists  love  to 
dwell.  But  this  is  not  the  real  question.  Their  ignoratio 
elenchi  consists  in  multiplying  proofs  that  slow-working 
causes  might  have  effected  all  these  stupendous  results, 
and  then  jumping  at  the  Conclusion  that  these  causes 
did  so  produce  them.  They  propound  this  Dilemma :  — 
Accept  this  solution  of  the  problem,  or  propose  a  better 
one.  We  may  logically  decline  to  do  either.  An  ingeni- 
ous mechanic,  witnessing  for  the  first  time  the  uniform 
motion  of  the  hands  over  the  dial-plate  of  a  clock,  if  chal- 
lenged to  explain,  without  inspecting  the  works,  how  this 
equable  and  long-continued  motion  could  be  produced, 
might  easily  invent  a  combination  of  springs,  wheels,  and 
pinions,  which  would  be  adequate  for  the  purpose ;  but  it 
would  be  extravagant  for  him  to  assume  that  the  machin- 
ery thus  invented  by  himself  was  an  exact  copy  of  the 
works  which  he  had  not  been  allowed  to  examine.  He 
could  only  say,  the  results  in  question  might  be  brought 
about  by  my  apparatus;  but  I  cannot  tell  how  they  are 
actually  produced.  Science  does  not  rest  on  hypothesis, 
and  is  not  content  with  possible  explanations  of  phenomena. 
The  well-known  rule  in  controversy,  that  the  burden  of 
proof  rests  on  him  who  maintains  the  affirmative,  because 
it  is  difficult,  or  impossible,  to  prove  a  negative,  rests  on 
the  considerations  here  alleged.  In  order  to  prove  a  nega- 
tive, it  must  be  demonstrated  that  not  one  out  of  many 
different  contingencies  admits  the  positive.  Thus  a  survey 
of  the  whole  field  is  necessary,  and  the  exclusion  of  the 
opposite  hypothesis  from  every  point  in  it  must  be  made 


OF  FALLACIES.  303 

certain.  On  the  other  hand,  the  proof  of  the  positive  is 
established  at  a  single  point ;  no  wide  range  of  search  is 
requisite.  To  borrow  an  illustration,  it  is  easy  to  demon- 
strate that  the  book  is  in  the  room ;  we  have  only  to  pro- 
duce it.  But  to  prove  that  it  is  not  there,  "  it  must  be 
made  certain,  first,  that  every  book  in  the  room  has  been 
found  and  examined,  secondly,  that  it  has  been  correctly 
examined.  No  one,  in  fact,  can  prove  more  than  that  he 
cannot  find  the  book ;  whether  the  book  be  there  or  not,  is 
another  question,  to  be  settled  by  our  opinion  of  the  vigi 
lance  and  competency  of  the  searcher."  The  geologists 
say  their  opponents  cannot  find  any  proof  that  the  ordinary 
working  of  Nature's  laws  could  not,  in  an  indefinite  lapse 
of  years,  produce  the  effects  in  question.  What  is  that  to 
the  purpose  ?  Our  inability  to  find  a  needle  in  a  hay-mow 
is  no  proof  that  the  needle  is  not  there. 

Indirectly,  indeed,  many  negatives  are  established  by  a 
single  positive ;  it  is  thus  that  an  accused  person  in  court 
makes  a  triumphant  defence  by  proving  what  the  lawyers 
call  an  alibi ;  direct  testimony  that  he  was  in  Manchester, 
on  the  night  in  question,  is  an  indirect  demonstration  that 
he  was  not  in  any  part  of  Birmingham,  where  the  crime 
must  have  been  committed.  Here,  the  testimony  required 
is  positive  in  character,  though  it  tends  indirectly  to  a  nega- 
tive result ;  hence,  it  is  easily  obtained.  Sometimes,  in- 
deed, when  there  are  but  few  possible  cases,  so  that  the 
field  for  search  is  very  limited,  we  may  be  required  to 
prove  a  negative  directly.  This  is  the  nature  of  the  ge- 
ometer's demonstration  per  impossibile,  as  it  is  called.  Fail- 
ing O  obtain  direct  proof  that  the  angle  A  is  equal  to  the 
angle  B,  we  remember  that  only  three  suppositions  are  pos- 
sible ;  and  then,  by  demonstrating  that  it  cannot  be  either 
greater  or  less,  we  indirectly  prove  that  it  must  be  equal. 
In  like  manner,  after  it  has  been  proved  that  the  accused 
person  committed  a  homicide,  it  is  a  presumption  in  law 


304  *  OF   FALLACIES. 

that  the  act  was  done  "with  malice  prepense";  in  other 
words,  the  law  puts  upon  the  accused  the  burden  of  proof 
that  he  did  not  do  it  maliciously.  But  this  seemingly  harsh 
presumption  of  law  rests,  as  Mr.  De  Morgan  remarks,  upon 
the  fact,  that  there  are  so  few  alternatives  to  the  supposi- 
tion of  wilful  murder ;  in  order  to  disprove  malice,  the 
accused  is  only  required  to  make  out  either  mishap,  insan- 
ity, or  heat  of  blood.  He  is  not  put  to  hunting  for  a  needle 
in  a  hay-mow,  under  penalty  of  being  hanged  if  he  fails ; 
but,  out  of  four  possible  cases,  he  is  obliged  to  disprove  the 
single  fatal  supposition  by  direct  evidence  that  his  case  is 
some  one  of  the  three  others. 

Most  rhetorical  artifices  may  be  referred  to  the  class  of 
the  ignoratio  elenchi.  Thus,  says  Dr.  Whately,  "  when 
the  occasion  or  object  in  question  is  not  such  as  calls  for,  or 
as  is  likely  to  excite  in  those  particular  readers  or  hearers, 
the  emotions  required,  it  is  a  common  rhetorical  artifice  to 
turn  their  attention  to  some  object  which  will  call  forth 
these  feelings ;  and  when  they  are  too  much  excited  to  be 
capable  of  judging  calmly,  it  will  not  be  difficult  to  turn 
their  passions,  once  roused,  in  the  direction  required,  and 
to  make  them  view  the  case  before  them  in  a  very  different 
light.  When  the  metal  is  heated,  it  may  easily  be  moulded 
into  the  desired  form.  Thus,  vehement  indignation  against 
some  crime  may  be  directed  against  a  person  who  has  not 
been  proved  guilty  of  it ;  and  vague  declamations  against 
corruption,  oppression,  &c,  or  against  the  mischiefs  of 
anarchy,  with  high-flown  panegyrics  on  liberty,  rights  of 
man,  &c,  or  on  social  order,  justice,  the  constitution,  law, 
religion,  &c,  will  gradually  lead  the  hearers  to  take  for 
granted,  without  proof,  that  the  measure  proposed  will  lead 
to  these  evils,  or  to  these  advantages ;  and  it  will  in  con- 
sequence become  the  object  of  groundless  abhorrence  or 
admiration. " 

Under  this  class  of  Fallacies  also  may  be  ranked  the 


OF  FALLACIES.  305 

error  of  adopting  a,i  argument  which  proves  either  too  little 
or  too  much.  In  one  of  these  cases,  however,  the  error  is 
by  no  means  so  serious  as  in  the  other.  The  reasoning 
which  proves  too  little  may  be  good  as  far  as  it  goes  ;  it 
conduces  to  the  end  in  view,  and,  taken  in  conjunction 
with  another  argument  also  partial  in  its  effect,  it  may 
establish  the  whole  doctrine  in  question.  But  the  argu- 
ment which  proves  too  much  is  invalid  throughout ;  Falsus 
in  uno,  falsus  in  omnibus,  is  a  sound  logical  maxim.  If 
any  portion  of  the  Conclusion  is  evidently  false,  the  rea- 
soning which  led  to  it,  considered  in  itself  alone,  must 
be  essentially  and  altogether  vicious;  since  from  correct 
premises,  and  by  valid  inference,  no  error  whatever  can 
possibly  be  deduced. 

When  the  main  purpose  is  to  disprove  a  particular  doc- 
trine, it  is  not  enough  to  refute  one  or  more  arguments 
that  have  been  alleged  in  its  support ;  this  is  merely  con- 
futing your  opponent,  and  not  the  proposition  which  he 
maintains,  and  which  may  be  supported  by  better  reasons 
than  he  has  been  able  to  adduce.  In  like  manner,  to  state 
objections,  though  they  may  be  perfectly  valid  ones,  to  a 
specific  plan  of  action,  is  insufficient  to  prove  that  this  plan 
ought  to  be  rejected ;  for  it  may  well  be  that  some  action 
is  unavoidable,  and  yet  that  strong  objections  may  be  urged 
against  every  mode  of  action  that  can  be  devised.  When 
the  Necessitarian  says  that  the  doctrine  of  the  freedom  of 
the  human  will  is  inconceivable,  Sir  William  Hamilton 
justly  replies,  that  the  argument  proves  too  little  ;  for  it  is 
at  least  equally  inconceivable  that  the  will  should  not  be 
free.  Unbelievers,  says  Dr.  Whately,  "  may  find  numer- 
ous objections  against  various  parts  of  Scripture,  to  some 
of  which  no  satisfactory  answer  can  be  given  ;  and  the 
incautious  hearer  is  apt,  while  his  attention  is  fixed  on 
these,  to  forget  that  there  are  infinitely  more  and  stronger 
objections  against  the  supposition  that  the  Christian  religion 


306  OF   FALLACIES. 

is  of  human  origin ;  and  that,  where  we  cannot  answer  all 
objections,  we  are  bound  in  reason  and  in  candor  to  adopt 
the  hypothesis  which  labors  under  the  least." 

3.  A  full  illustration  of  the  Fallacy,  non  causa  pro  causa, 
would  carry  us  too  far  into  the  domain  of  the  physical 
sciences,  and  therefore  would  be  more  in  place  as  a  chapter 
of  Applied  Logic.  Only  the  more  frequent  and  obvious 
errors  of  this  class  can  be  noticed  here.  Prominent  among 
these  are  the  common  blunders  of  reasoning  post  hoc,  ergo 
propter  hoc;  of  mistaking  physical  laws  for  efficient  causes  ; 
and  of  applying  the  doctrine  of  the  Necessitarian  or  Fatalist 
as  a  motive  of  action,  or  rather  of  inaction,  in  our  ordinary 
concerns. 

An  invariable  antecedent  is  a  sign,  but  often  it  is  indis- 
putably not  a  cause,  of  the  phenomenon  which  it  precedes. 
As  that  which  leads  the  mind  to  expect  a  certain  event,  it 
mav  be  regarded  as  a  causa  cognoscendi ;  but  this  is  very 
different  from  the  causa  essendi,  which  is  the  ordinary  sig- 
nification of  the  word  cause.  Cicero  states  this  distinction 
very  clearly :  —  Causa  autem  ea  est  quce  id  efficit  cujus  est 
causa.  Non  sic  causa  intelligi  debet,  ut,  quod  cuique  ante-' 
cedat,  id  ei  causa  sit,  sed  quod  cuique  efficienter  antecedat. 
In  this  sense,  deliberation  is  certainly  not  the  cause  of  the 
action  which  follows  it,  nor  is  one  beat  of  the  pulse  the 
cause  of  the  subsequent  beats.  In  fact,  two  successive 
states  of  the  same  substance  are  seldom  regarded  even  by 
the  vulgar  as  cause  and  effect.  But  since  we  necessarily 
think  a  cause  as  immediately  preceding  its  effect,  or  as 
simultaneous  with  it,  the  mind  is  prone,  especially  in  the 
case  of  obscure  and  anomalous  phenomena,  of  which  the 
true  cause  cannot  easily  be  discovered,  to  consider  any  an- 
tecedent event  as  such  a  cause.  This  is  the  origin  of  the 
belief  in  omens,  and  many  other  superstitions  of  the  vulgar. 
An  accidental  conjunction  in  time  between  some  private 
or  public  calamity,  and  the  appearance  of  a  meteor  or  a 


OF   FALLACIES.  307 

comet,  or  the  occurrence  of  an  earthquake,  is  regarded  as 
indicating  a  causal  union  of  the  two  events.  The  science 
of  medicine,  at  least  in  that  branch  of  it  which  is  called 
therapeutics,  is  little  else  than  an  application  of  the  maxim, 
Post  hoc,  ergo  propter  hoc.  The  wisest  physician  cannot 
tell,  in  any  one  case,  whether  the  recovery  of  the  patient 
took  place  because  he  swallowed  the  drugs,  or  in  spite  of 
them,  or  whether  they  were  powerless  in  respect  either  to 
good  or  evil.  A  harsh  application  of  this  fallacious  rule 
consists  in  judging  the  wisdom  of  a  man's  conduct  by  its 
consequences,  or  the  uprightness  of  his  intentions  by  the 
immediate  results  of  his  action  upon  the  happine'ss  or 
misery  of  those  around  him.  A  brave  and  able  com- 
mander is  not  always  successful  in  battle,  and  a  consci- 
entious and  kind-hearted  man  may  be  compelled  by  a 
sense  of  duty  to  inflict  suffering  and  death.  Practical 
men,  as  they  are  called,  who  profess  to  be  guided  only  by 
experience,  and  to  rely  upon  facts  instead  of  theories,  are 
especially  liable  to  this  class  of  errors.  In  their  eyes,  the 
disorders  and  other  evils  which  follow  some  long-delayed 
reform  are  attributable  to  the  reform  itself,  and  not  to  its 
undue  postponement. 

Forming  an  induction  from  too  small  a  class  of  cases, 
and  disregarding  negative  instances,  are  the  frequent 
source  of  this  confusion  between  an  antecedent  phenome- 
non and  an  efficient  cause.  The  most  common  of  all  the 
superstitions  of  the  vulgar,  the  belief  that  Friday  is  an 
unlucky  day  for  beginning  any  new  enterprise,  may  be 
traced  to  this  origin.  And  it  should  not  be  forgotten,  that 
the  prognostications  of  evil  thus  formed  very  often  bring 
about  their  own  fulfilment ;  fearful  and  dispiiited  men 
can  make  little  effectual  effort  to  avert  danger.  The 
belief  in  the  hereditary  transmission  of  diseases  of  mind 
and  body,  at  least  in  the  unreasonable  extent  to  which  it 
new  prevails,  is  formed  in  this  manner,  and  tends  in  tins 


308  OF  FALLACIES. 

way  to  verify  itself.  Gout  and  insanity  run  in  families 
where  a  perpetual  apprehension  of  them  exists,  and  where, 
perchance,  habits  of  life  are  actually  transmitted  from 
father  to  son  which  are  likely  to  induce  and  foster  such 
diseases.  But  even  in  these  cases,  a  careful  enumeration 
might  satisfy  one  that,  of  all  who  are  within  the  unlucky 
circle,  at  least  as  many  escape  the  dreaded  calamity  as 
those  who  suffer  from  it.  Were  it  otherwise,  indeed,  the 
circle  would  continue  to  enlarge  itself  in  successive  gener- 
ations, till  few  could  hope  to  escape  the  hereditary  taint. 
As  Dr.  Johnson  remarks,  the  one  prophetic  dream  which 
comes  to  pass  is  remembered  and  spoken  of,  while  the 
ninety  and  nine  which  fail  of  accomplishment  are  for- 
gotten. 

"  In  minds  not  habituated  to  accurate  thinking,"  says 
Mr.  Mill,  "  there  is  often  a  confused  notion  that  the  gen- 
eral laws  are  the  causes  of  the  partial  ones ;  that  the  law 
of  general  gravitation,  for  example,  causes  the  phenomenon 
of  the  fall  of  bodies  to  the  earth.  But  to  assert  this  would 
be  a  misuse  of  the  word  cause;  terrestrial  gravity  is  not 
an  effect  of  general  gravitation,  but  a  case  of  it ;  that  is, 
one  kind  of  the  particular  instances  in  which  that  general 
law  obtains."  A  Law  of  Nature  is  only  a  general  fact,  or, 
rather,  a  general  statement  comprehending  under  it  many 
similar  individual  facts.  Hence,  such  a  Law  does  not  ac- 
count for,  or  explain,  the  phenomena  of  Nature ;  it  only 
describes  them.  Thus,  it  is  not  a  Law  of  Hydrostatics 
which  causes  water  to  remain  at  the  same  level  in  the  two 
arms  of  a  bent  tube ;  but  the  fact  that  water  stands  at  this 
level  is  ranked  among  many  other  facts,  which  are  com- 
prehended under  the  general  statement  called  a  Law  of 
Hydrostatics. 

The  process  of  Thought  by  which  we  pass  from  a  Phys- 
ical Law  to  an  individual  case  happening  under  it  is  one 
of  Deduction,  and  is  therefore  governed  by  the  dictum*  di 


OF   FALLACIES.  309 

omni.  Because  all  bodies  tend  to  fall  towards  the  common 
centre  of  gravity,  therefore  this  body  thus  tends  to  fall. 
Hence,  the  statement  of  the  Law  is  that  which  makes  us 
believe  that  the  individual  event  will  happen ;  and  this,  by 
a  very  natural  confusion  of  Thought,  is  mistaken  for  the 
cause  which  makes  the  event  happen.  But  the  relation  in 
the  former  case  is  that  between  Premises  and  Conclusion ; 
in  the  latter,  between  Cause  and  Effect ;  the  former  is  a 
law  of  Thought,  the  latter  is  a  law  of  things ;  the  one  is 
the  causa  cognoscendi,  the  other,  the  causa  essendi. 

The  Fallacy  here  exposed  is  one  of  much  interest,  as  it 
is  that  which  lies  at  the  bottom  of  every  scheme  of  Materi 
alism,  —  every  attempt  to  account  for  the  origin  of  species, 
and  the  general  phenomena  of  the  universe,  without  bring- 
ing in  any  other  agency  than  that  of  mere  Physical  Laws, 
or  what  it  was  once  the  fashion  to  call  "  Second  Causes." 
Such  a  theory  is  not  only  insufficient,  or  unsupported  by 
the  requisite  evidence ;  it  is  founded  upon  a  mere  confusion 
of  Thought,  and  is  illogical  and  absurd.  There  is  no  such 
thing  as  the  agency  or  action  of  a  Law ;  except  as  a  figure 
of  speech,  we  might  as  well  predicate  locomotion  of  an  idea, 
or  speak  of  bilateral  triangles.  "  Second  Causes  "  are  no 
causes  at  all ;  they  are  mere  fictions  of  the  intellect,  and 
exist  only  in  Thought.  A  cause  in  the  proper  sense  of  the 
word,  that  is,  an  efficient  cause,  as  original  and  direct  in  its 
action,  must  be  a  First  cause ;  that  through  which  its  ac- 
tion is  transmitted  is  not  a  cause,  but  a  portion  of  the 
effect,  —  as  it  does  not  act,  but  is  acted  upon. 

The  Ignava  Ratio,  or  do-nothing  argument,  is  a  falla- 
cious application  of  the  Necessitarian  theory.  According 
to  this  theory,  all  occurrences  whatever  have  their  environ- 
ment of  circumstances,  with  which  they  stand  in  neces- 
sary and  fixed  relations  by  an  absolute  law^  and  the  state 
of  the  universe  at  any  one  moment,  in  all  its  parts,  from 
the  creation  of  a  world  to  the  stirring  of  an  aspen-leaf,  coidd 


310  OF   FALLACIES. 

not  possibly  have  been  different  from  what  is.  Every  oc- 
currence has  its  cause,  of  which  it  is  the  necessary  result, 
and  to  which  it  is  necessarily  proportioned,  even  in  the 
minutest  respects.  Every  event,  of  course,  is  surrounded 
by  oth^r  events,  and  must  be  considered  as  being  at  the 
same  time  both  antecedent  and  consequent,  —  as  necessa- 
rily resulting  from  those  which  preceded  it,  and  neces- 
sarily followed  by  those  which  come  after  it,  —  and  thus 
as  forming  one  link  in  an  adamantine  chain  which  extends 
from  eternity  to  eternity.  As  Mr.  Mill  himself,  an  en- 
lightened and  consistent  advocate  of  this  theory,  remarks, 
"  there  is  no  Thing  produced,  no  event  happening,  in  the 
known  universe,  which  is  not  connected  by  a  uniformity, 
or  invariable  sequence,  with  some  one  or  more  of  the 
phenomena  which  preceded  it ;  insomuch  that  it  will  hap- 
pen again  as  often  as  these  phenomena  occur  again,  and 
as  no  other  phenomenon  having  the  character  of  a  counter- 
acting cause  shall  coexist.  These  antecedent  phenomena, 
again,  were  connected  in  a  similar  manner  with  some  that 
preceded  them ;  and  so  on,  until  we  reach,  as  the  ultimate 
step  attainable  by  us,  either  the  properties  of  some  one 
primeval  cause,  or  the  conjunction  of  several.  The  state 
of  the  whole  universe  at  any  instant  we  believe  to  be  the 
consequent  of  its  state  at  the  previous  instant ;  insomuch 
that  one  who  knew  all  the  agents  which  exist  at  the  pres- 
ent moment,  their  collocation  in  space,  and  their  properties, 
—  in  other  words,  the  laws  of  their  agency,  —  could  pre- 
dict the  whole  subsequent  history  of  the  universe,  at  least 
unless  some  new  volition  of  a  power  capable  of  controlling 
the  universe  should  supervene."  * 

The  confutation  of  this  astounding  theory  is  the  business 
of  the  metaphysician  or  the  theologian ;  we  have  no  con- 
cern with  it  here,  except  to  point  out  the  Fallacy  of  re- 
garding it  as  justifying  inaction,   or  as  demonstrating  the 

«  Mill's  Logic,  3d  ed.,  Vol.  I.  p.  358. 


OF  FALLACIES.  311 

hopelessness  of  any  endeavor  ,on  our  part  to  control  the 
course  of  natural  events.  The  Ignava  Ratio  is  thus  stated 
hy  Cicero,  in  the  form  of  an  argument  against  taking  any 
measures  for  the  restoration  of  one's  health. 

If  it  is  fated  that  you  shall  recover  from  the  present  disease,  then 
you  will  recover  whether  you  call  in  a  physician  or  not. 
If  it  is  fated  that  you  shall  not  recover,  then,  with  or  with- 
out a  physician,  you  will  not  recover. 

But  either  the  one  or  the  other  of  these  two  contradictories  is 
fated. 

Therefore,  it  will  be  of  no  use  to  call  in  a  doctor. 

As  Cicero  remarks,  if  this  reasoning  were  correct,  our 
whole  life  would  be  reduced  to  a  state  of  hopeless  inactiv- 
ity ;  as  it  would  prove  the  inutility  of  any  endeavor  to 
bring  about  a  desirable  result,  or  to  avert  a  threatened 
calamity.  The  Turks,  who  are  fatalists,  so  understand  it, 
and  reduce  it  to  practice  by  refusing  to  take  any  precau- 
tions against  a  pestilence,  or  to  remove  a  lighted  match 
from  its  dangerous  proximity  to  a  powder-magazine.  But 
they  only  show  thereby  that  they  are  incapable  of  follow- 
ing out  correctly  the  logical  consequences  of  their  own  doc- 
trine. Calling  in  medical  aid  furnishes  a  new  antecedent, 
and  thus  presents  a  new  case  for  the  determination  of  Fate. 
It  may  also  be  fated  that  I  should  send  for  a  physician,  and, 
with  his  aid,  that  I  should  recover ;  or  it  may  be  fated  that 
he  should  not  be  called  in,  and,  as  a  consequence  of  this 
neglect,  and  not  as  a  necessary  result  of  the  disease  alone, 
that  I  should  die.  Fate  is  only  a  concurrence  of  causes 
and  an  assemblage  of  conditions ;  supply  a  new  cause,  take 
away  one  of  the  necessary  conditions,  and  the  result  will 
be  different,  though  it  will  still  be  a  fated  or  necessary 
result.  Zeno  aptly  confuted  this  Fallacy,  when  he  was 
whipping  a  slave,  who  called  out,  in  excuse  for  his  fault, 
that  it  was  fated  for  him  to  steal ;  "  And  so  it  is  for  me  to 
whip  you,"  was  the  reply. 


812  OF  FALLACIES. 

Most  of  the  sophisms  once,  called  Inexplicable  have  been 
already  resolved  in  treating  of  the  different  classes  of  Fal- 
lacies to  which  they  were  respectively  referred.  It  is  only 
necessary  to  consider  here  the  famous  argument,  called  the 
Achilles,  proposed  by  Zeno  the  Eleatic,  as  Mr.  Mansel  says, 
"  to  support  the  leading  tenet  of  Parmenides,  of  the  unity 
of  all  things,  by  showing  that  the  identity  of  rest  and  mo- 
tion is  a  necessary  result  from  the  contrary  opinion."  It 
might  more  aptly  be  adduced  to  prove  that  extension  is  n^t 
infinitely  divisible,  for  if  it  were  so,  according  to  this  argu- 
ment, motion  would  be  impossible.  The  sophism  is  thus 
stated. 

The  swiftest  runner  can  never  overtake  the  slowest,  if 
the  latter  has  ever  so  little  the  start.  Suppose,  for  instance, 
that  Achilles  runs  ten  times  as  fast  as  a  tortoise,  and  that 
the  tortoise  is  one  mile  in  advance  at  the  outset.  While 
Achilles  is  traversing  this  mile,  the  tortoise  has  advanced 
T^th  of  a  mile  farther ;  before  his  pursuer  has  passed  over 
this  -j^th,  the  tortoise  has  advanced  y^th,  and  then,  again, 
l0100th,  and  so  on  forever,  always  being  some  fraction, 
however  small,  of  a  mile  in  advance. 

Dr.  Whately  seems  to  have  been  entirely  puzzled  by 
this  sophism,  as  he  does  not  attempt  a  solution  of  it,  but 
merely  remarks  that  it  "furnishes  a  confirmation  of  the 
utility  of  an  acquaintance  with  the  Syllogistic  form,  in 
which  form  the  pretended  demonstration  cannot  possibly 
be  expressed."  But  this  confession,  as  Mr.  Mansel  ob- 
serves, "is  in  fact  a  surrender  of  the  Syllogistic  criterion, 
as  a  means  of  discriminating  between  sound  and  unsound 
reasoning.  On  the  contrary,  nothing  is  easier  than  to  ex- 
hibit the  reasoning  in  a  Syllogism,  and  to  show  thereby 
that  the  fallacy  does  not  lie  in  the  Form,  but  the  Matter. 
Thus,  representing  the  whole  space  to  be  traversed  by  a, 

4  Any  space  equal  to  —  -f-  —  +  77^'  &c*  is  infinite  (being  the 
sum  of  an  infinite  series). 


OF  FALLACIES.  313 

'The  space  to  be  passed  before  Achilles  overtakes  the  tortoise  is 

equal  to  this  sum. 
'  Therefore,  it  is  infinite/ 

"  The  whole  logical  mystery  of  this  famous  Fallacy  lies 
in  this,  that  the  major  premise  is  false.  The  sum  of  an 
infinite  series  may  be,  and  in  this  case  is,  finite.  This 
premise  is  equally  false,  whether  space  is,  or  is  not,  divis- 
ible ad  infinitum."  * 

Fries  remarks  that  the  sophistry  is  here  covered  up  by 
the  mode  of  stating  the  problem.  The  question  really 
asked  is,  when  will  Achilles  have  passed  over  the  particular 
extent  of  ground  which  the  tortoise,  at  any  one  moment,  has 
already  left  behind  him;  and  this*  question,  on  account  of 
the  infinite  divisibility  of  space  and  time,  may  be  repeated 
ad  infinitum.  The  true  question,  at  what  point  will  Achil- 
les overtake  the  tortoise,  is  not  allowed  to  come  into  view. 
The  space  between  the  two  parties,  however  small,  is,  in 
thought,  though  not  in  reality,  infinitely  divisible ;  and  the 
series  of  constantly  diminishing  terms  into  which  it  is 
mentally  broken  up,  though  infinite  in  number,  is  finite  in 
amount,  the  sum  of  the  series  being  equal,  of  course,  only 
to  the  small  space  originally  divided.  Any  finite  quantity 
may  be  broken  up  into  an  infinite  number  of  terms,  if  these 
terms  become  infinitely  small.  The  confusion  of  thought 
consists  in  mistaking  the  sum  of  the  terms  of  such  a  de- 
scending series,  composed  of  infinitesimals,  for  the  sum  of 
an  infinite  series  the  terms  of  which  are  not  infinitely  small. 
It  is  only  this  latter  sum  which  is  necessarily  an  infinite 
quantity. 

*  Mansel's  Notes  to  Aldrich,  pp.  141,  142. 


14 


314  APPLIED  LOGIC. 


CHAPTER    X 


APPLIED  LOGIC. 


APPLIED  Logic,  as  it  will  be  here  understood,  includes 
both  what  has  usually  been  called  the  Doctrine  of 
Method,  and  what  Sir  William  Hamilton  terms  Modified 
Logic.  Its  object  is  the  proper  regulation  of  the  Thinking 
Faculty,  not  only  in  forming  individual  cognitions,  but  in 
the  more  complex  processes  required  for  the  construction 
and  advancement  of  Science.  Pure  Logic,  as  we  have 
seen,  is  concerned  only  with  the  Forms  of  Thought ;  it 
considers  these  as  given,  or  already  formed,  and  regards 
only  the  necessary  and  fundamental  laws,  emanating  from 
the  mind  itself,  which  have  concurred  in  their  formation 
and  which  regulate  their  use.  Applied  Logic  has  regard 
also  to  the  Matter  of  Thought,  —  to  the  infinitely  numer- 
ous and  diversified  objects  of  cognition  which  Nature  fur- 
nishes us,  —  and  considers  by  what  general  processes  these 
are  brought  within  the  grasp  of  mind,  or  are  made  intelli- 
gible, or,  what  is  the  same  thing,  are  put  under  the  Forms 
of  Thought.  The  laws  which  govern  these  processes  are 
not  universal  and  necessary,  as  in  the  former  case,  but  are 
contingent  and  varied,  depending,  in  part,  on  the  diverse 
and  multiform  characteristics  of  the  objects  of  cognition, 
and,  in  part,  on  the  powers  and  limitations  of  the  human 
mind  itself.  To  avoid  the  vagueness  and  perplexity  which 
result  from  attempting  to  grasp  too  much,  Applied  Logic 
treats  directly  only  of  the  latter,  —  that  is,  of  the  formation 
of  Science  so  far  as  this  depends  on  the  nature  of  the  human 


APPLIED  LOGIC.  315 

intellect,  leaving  to  the  special  sciences  the  duty  of  adapt- 
ing their  own  procedures  to  the  nature  of  the  peculiar 
objects  of  study  with  which  they  are  immediately  con- 
cerned. 

This  division,  however,  like  many  others  in  Science,  can- 
not be  always  accurately  preserved.  The  processes  through 
which  the  mind  acts  can  be  exemplified  only  in  their  appli- 
cation to  various  classes  of  objects,  and  as  varying  some- 
what with  the  nature  of  those  objects.  The  practical  dis- 
tinction will  be,  that  Applied  Logic  regards  the  peculiarities 
of  what  we  are  thinking  about  only  so  far  as  these  illustrate, 
and  in  some  measure  direct,  the  processes  of  thinking.  It 
considers  primarily  how  the  mind  acts,  and  only  secondarily 
what  it  is  acting  upon. 

Science  is  a  body  of  truths  relating  to  any  well-defined 
object  or  class  of  objects,  so  arranged  as  to  be  easily  com 
prehended  and  retained,  and  conveniently  used.  The  mer- 
its at  which  it  aims  are  Completeness,  Thoroughness,  and 
Method.  Its  objects  are  the  numberless  things  which  Na- 
ture furnishes  us  for  study. 

What  we  call  Nature  is  an  assemblage  of  objects  and  a 
succession  of  events.  The  mind,  on  account  of  the  limita- 
tion of  its  faculties,  and  the  endless  number  and  variety  of 
these  objects  and  events,  cannot  grasp  and  consider  them 
all  at  once.  Neither  can  it  undertake  to  study  successively 
each  individual  thing  by  itself ;  for  a  lifetime  might  be  so 
spent,  before  we  could  obtain  even  a  small  fraction  of  the 
knowledge  which  is  requisite  for  the  proper  guidance  of  life. 
The  first  necessity,  then,  which  is  imposed  upon  us  by  the 
constitution  of  the  mind  itself,  is  to  break  up  the  infinite 
wealth  of  Nature  into  groups  and  classes  of  things,  with 
reference  to  their  resemblances  and  affinities,  and  thus  to 
enlarge  the  grasp  of  our  mental  faculties,  even  at  .the  ex- 
pense of  sacrificing  the  minuteness  of  information  which 
can  be  acquired  only  by  studying  objects  in  detail.     The 


316  APPLIED   LOGIC. 

first  efforts  in  the  pursuit  of  knowledge,  then,  must  be 
directed  to  the  business  of  Classification.  Perhaps  it  will 
be  found  in  the  sequel,  that  Classification  is  not  only  the 
beginning,  but  the  culmination  and  the  end,  of  human 
knowledge. 

We  will  first  consider  the  mental  processes  through  which 
we  gain  a  knowledge  of  real  Objects,  —  that  is,  of  Objects 
which  coexist  in  space,  leaving  for  subsequent  inquiry  the 
question,  how  far  these  processes  must  be  modified  in  con- 
structing a  science  of  Events  which  succeed  each  other  in 
time. 

It  has  already  been  remarked,  that  the  beginning  of  all 
knowledge  is  in  single  acts  of  the  Perceptive  or  Acquisitive 
Faculty,  which  operates  either  through  the  external  senses, 
thus  constituting  External  Perception,  or  through  that  no- 
tice which  the  mind  takes  of  what  is  passing  within  itself, 
this  being  denominated  Consciousness,  or  Internal  Percep- 
tion. In  either  case,  one  indivisible  act  of  the  Perceptive 
Faculty  gives  us  to  know  only  one  phenomenon.  A  suc- 
cession of  such  acts  relating  to  one  Object  furnishes  a  num- 
ber of  cognitions  of  the  qualities  or  attributes  of  that  Ob- 
ject; and  these  qualities  we  unite  together,  and  bind  up 
into  one  whole,  through  the  conception,  which  the  mind 
furnishes,  of  Substance,  or  that  in  which  the  qualities  inhere. 
Thus,  suppose  the  Object  presented  is  an  apple ;  the  eye 
tells  me  that  it  is  red ;  the  touch,  that  it  is  spherical  and 
moderately  hard ;  the  muscular  sense,  that  it  has  weight; 
the  taste,  that  it  is  subacid,  &c. ;  and  these  qualities  I  unite 
into  one  whole  by  the  conception  of  one  substance  in  which 
they  all  inhere,  and  call  the  aggregate  thus  formed  apple. 
The  reason  why  just  these  qualities,  and  no  others,  are 
united  into  the  whole  is,  that  they  all  are,  or  may  be, 
received  at  one  time,  under  the  same  circumstances,  and 
appear  to  proceed  from  one  Object,  as  they  are  referred  by 
me  to  one  definite  locality  in  space. 


APPLIED   LOGIC.  317 

Take  another  instance  from  Internal  Perception.  I  am 
conscious,  either  at  once  or  in  succession,  of  joy  or  pain,  of 
a  thought,  reminiscence,  or  volition,  of  a  sensation  of  hun- 
ger, coldness,  &c.  ;  and  these  separate  Intuitions  I  put 
together  into  one  whole  through  the  Intuition,  which  enters 
into  each  of  them,  that  they  are  mine,  or  that  they  all  be- 
long to  the  one  person  which  I  call  myself.  Here,  the  Intui- 
tion of  Self  is  the  unifying  principle,  or  that  through  which 
the  aggregation  of  many  into  one  is  accomplished,  just  as, 
in  the  former  case,  it  was  the  conception  of  Substance. 

Manifestly,  then,  the  first  step  towards  the  formation  of 
science  is  a  Synthesis,  a  putting  together  of  the  Matter  of 
several  Intuitions  into  that  one  whole  which  we  call  an 
Individual  Object.  This  Object  itself,  though  called  an  In- 
dividual, as  if  it  were  one  thing,  has  in  truth  only  a  virtual 
unity ;  it  is  really  complex,  consisting  of  many  parts  and 
many  qualities,  which  were  at  first  separately  perceived ; 
but  having  often  been  perceived  together,  or  in  combina- 
tion, they  become  so  firmly  united  that  the  perception  of  a 
few,  perhaps  of  only  one,  of  its  parts  or  qualities  immedi- 
ately calls  up  the  imagination  of  all  the  others,  that  is,  of 
the  whole.  Thus,  I  am  said  to  perceive  the  apple,  when, 
in  fact,  I  perceive  only  its  shape  and  color ;  but  this  shape 
and  color  immediately  suggest  all  its  other  qualities,  and 
the  complex  Intuition  thus  formed,  partly  perceived  and 
partly  imagined,  is  what  is  called,  though  improperly,  a 
single  perception  of  one  thing.  The  wholes  thus  formed 
are  of  all  degrees  of  complexity,  either  having  as  many 
parts,  qualities,  and  uses  as  a  house  or  an  intricate  machine, 
or  as  few  as  a  spot  of  purple  cloud  in  the  sky.  They  may 
be  either  real  or  factitious,  the  conception  and  belief  of 
actual  existence  being  one  of  the  parts  or  elements  of  the 
former,  but  not  of  the  latter.  Each  of  these  wholes  is,  or 
might  be,  designated  by  a  Proper  Name,  belonging  to  this 
one  thing  and  to  nothing  else. 


318  APPLIED   LOGIC. 

But  as  the  number  of  such  Objects  and  Names  would  be 
endless,  we  seek,  as  has  been  said,  to  bring  them  within 
the  grasp  of  the  mind  by  throwing  them  into  groups  and 
classes.  The  first  step  of  the  process  directed  to  this  end 
is  the  reverse  of  the  former  one  ;  we  must  now  begin  by 
Analysis.  The  many  complex  wholes,  called  Individual 
Objects,  which  we  have  previously  formed  by  a  procedure 
so  easy  and  so  frequently  repeated  that  we  are  almost  un- 
conscious of  it,  must  now  be  resolved  into  their  constituent 
parts  and  properties,  in  order  that,  by  an  abstraction  of 
their  dissimilar  elements  and  restricting  the  attention  to 
those  which  are  similar,  classes  may  be  formed,  all  the 
members  of  which  have  some  like  or  equivalent  attributes. 
The  process  of  Classification,  then,  is  an  Analysis  immedi- 
ately followed  by  a  Synthesis  into  groups,  this  Synthesis 
being  directed  by  the  Comparative  or  Elaborative  Faculty 
of  the  mind,  the  chief  function  of  which  is  the  perception 
of  relations,  and  especially  the  relations  of  likeness  and 
unlikeness.  Having  formed  one  set  of  classes,  called  the 
Infimas  Species,  because  they  are  composed  of  Individuals 
only,  we  then  proceed,  in  an  exactly  similar  way,  to  group 
these  groups  into  Genera ;  and  so  on,  erecting  a  hierarchy 
of  Concepts,  until  we  at  least  approximate  a  Summum 
Genus,  or  that  thought  which  embraces  all  conceivable 
things.  The  highest  generalization  usually  attempted  is 
that  which  arranges  all  existence,  whether  actual  or  poten- 
tial, under  the  three  heads,  Man,  the  Universe,  and  God 
who  is  Absolute  Being  and  Absolute  Cause. 

Evidently,  then,  the  universal  procedure  of  Science  is 
an  Analysis  followed  by  a  Synthesis,  the  result  of  the 
whole  being  a  more  or  less  complete  Classification.  All 
the  problems  which  Science  has  to  solve  may  be  reduced 
to  these  two  questions :  What  Classes  ought  to  be  formed  ? 
and,  Does  this  or  that  Object  possess  the  special  attribute  or 
attributes  which  entitle  it  to  be  ranked  under  a  certain 


APPLIED  LOGIC.  319 

Class  ?  Isolated  cognitions  —  the  knowledge,  for  instance, 
that  this  particular  attribute  does,  or  does  not,  belong  to 
this  particular  thing  —  are  not  entitled  to  be  called  Sci- 
ence, until  they  are  arranged  in  some  Class,  or  subsumed 
under  some  comprehensive  Law. 

There  is  a  confusion  in  the  application  of  the  terms  Anal- 
ysis and  Synthesis,  which  may  be  best  resolved  by  bor- 
rowing a  passage  from  Sir  William  Hamilton.  "  It  is 
manifest,  in  general,  from  the  meaning  of  the  words,  that 
the  term  Analysis  can  only  be  applied  to  the  separation  of 
a  whole  into  its  parts ;  and  that  the  term  Synthesis  can 
only  be  applied  to  the  collection  of  parts  into  a  whole.  So 
far,  no  ambiguity  is  possible,  —  no  room  is  left  for  abuse. 
But  there  are  different  kinds  of  whole  and  parts  ;  some  of 
the  wholes,  like  the  whole  of  Comprehension  (called  also 
the  Metaphysical),  and  the  whole  of  Extension  (called  also 
the  Logical),  are  in  the  inverse  ratio  of  each  other;  so 
that  what  in  the  one  is  a  part,  is  necessarily  in  the  other  a 
whole.  It  is  evident,  then,  that  the  counter  processes  of 
Analysis  and  Synthesis,  as  applied  to  these  counter  wholes 
and  parts,  should  fall  into  one,  or  correspond ;  inasmuch  as 
each  in  the  one  quantity  should  be  diametrically  opposite  to 
itself  in  the  other.  Thus,  Analysis,  as  applied  to  Compre- 
hension, is  the  reverse  process  of  Analysis  as  applied  to 
Extension,  but  a  corresponding  process  with  Synthesis ; 
and  vice  versa.  Now,  should  it  happen  that  the  existence 
and  opposition  of  the  two  quantities  are  not  considered,  — 
that  men,  viewing  the  whole  of  Extension  or  the  whole  of 
Comprehension,  each  to  the  exclusion  of  the  other,  must 
define  Analysis  and  Synthesis  with  reference  to  that  sin- 
gle quantity  which  they  exclusively  take  into  account ;  — 
on  this  supposition,  I  say,  it  is  manifest  that,  if  different 
philosophers  regard  different  wholes  or  quantities,  we  may 
have  the  terms  Analysis  and  Synthesis  absolutely  used  by 
different  philosophers  in  a  contrary  or  reverse  sense.     And 


320  APPLIED   LOGIC. 

this  has  actually  happened.  The  ancients,  in  general, 
looking  only  to  the  whole  of  Extension,  use  the  terms 
Analysis  and  Synthesis  simply  to  denote  a  division  of  the 
Genus  into  Species,  —  of  the  Species  into  Individuals ;  the 
moderns,  on  the  other  hand,  in  general,  looking  only  at  the 
whole  of  Comprehension,  employ  these  terms  to  express  a 
resolution  of  the  Individual  into  its  various  attributes." 

The  words  analytic  and  synthetic,  Hamilton  further  ob- 
serves, "are,  like  most  of  our  logical  terms,  taken  from 
Geometry  "  ;  and  the  applications  of  them  in  this  science 
are  thus  admirably  illustrated  by  Dr.  W  he  well.  In  discur- 
sive processes  of  reasoning,  he  remarks,  "  we  obtain  our 
conclusions,  not  by  looking  at  our  conceptions  steadily 
in  one  view,  which  is  intuition,  but  by  passing  from  one 
view  to  another,  like  those  who  run  from  place  to  place 
(discursus).  Thus,  a  straight  line  may  be,  at  the  same 
time,  a  side  of  a  triangle  and  a  radius  of  a  circle ;  and  in 
the  first  proposition  of  Euclid,  a  line  is  considered  first  in 
one  of  these  relations,  and  then  in  the  other,  and  thus  the 
sides  of  a  certain  triangle  are  proved  to  be  equal.  And  by 
this  *  discourse  of  reason,'  as  by  our  older  writers  it  was 
termed,  we  set  forth  from  those  axioms  which  we  perceive 
by  intuition,  travel  securely  over  a  vast  and  varied  region, 
and  become  possessed  of  a  copious  store  of  mathematical 
truths."  In  such  geometrical  reasoning,  he  continues,  "  we 
introduce  at  every  step  some  new  consideration ;  and  it  is 
by  combining  all  these  considerations  that  we  arrive  at  the 
conclusion,  that  is,  the  demonstration  of  the  proposition. 
Each  step  tends  to  the  final  result,  by  exhibiting  some  part 
of  the  figure  under  a  new  relation.  To  what  we  have 
already  proved,  is  added  something  more ;  and  hence  this 
process  is  called  Synthesis,  or  putting  together.  The  proof 
flows  on,  receiving  at  every  turn  new  contributions  from 
different  quarters;  like  a  river  fed  and  augmented  by 
many  tributary  streams.      And  each  of  these  tributaries 


APPLIED  LOGIC.  321 

flows  from  some  definition  or  axiom  as  its  fountain,  or  is 
itself  formed  by  the  union  of  smaller  rivulets  which  have 
sources  of  this  kind.  In  descending  along  its  course,  the 
synthetical  proof  gathers  all  these  accessions  into  one  com- 
mon trunk,  the  proposition  finally  proved. 

"  But  we  may  proceed  in  a  different  manner.  We  may 
begin  from  the  formed  river,  and  ascend  to  its  sources. 
We  may  take  the  proposition  of  which  we  require  a  proof, 
and  may  examine  what  the  supposition  of  its  truth  implies. 
If  this  be  true,  then  something  else  may  be  seen  to  be 
true  ;  and  from  this,  something  else,  and  so  on.  We  may 
often,  in  this  way,  discover  of  what  simpler  propositions  our 
theorem  or  solution  is  compounded,  and  may  resolve  these 
in  succession,  till  we  come  to  some  proposition  which  is 
obvious.  This  is  geometrical  Analysis.  Having  succeeded 
in  this  analytical  process,  we  may  invert  it ;  and  may  de- 
scend again,  from  the  simple  and  known  propositions,  to  the 
proof  of  a  theorem,  or  the  solution  of  a  problem,  which  was 
our  starting-place."  * 

We  have  said  that  an  Individual  Object,  as  thought,  is  a 
Synthesis  of  parts  and  attributes.  But  it  is  not  an  arbi- 
trary Synthesis,  —  not  a  putting  together  of  any  elements 
whatever,  such  as  mere  caprice  may  have  induced  us  to 
select.  Imaginary  Objects,  it  is  true,  may  be  thus  built  up 
at  pleasure  ;  mere  fancy  may  construct  a  centaur,  a  griffin, 
or  any  other  imaginative  creation,  recognizing  it  at  the  mo- 
ment to  be  unreal.  But  if  actual  existence  is  one  of  the 
elements  of  the  combination,  that  is,  if  the  Object  thus 
thought  is  understood  to  be  a  real  Object,  our  conception  of 
it  must  be  a  Synthesis  of  such  parts  and  properties  only  as 
we  know  it  actually  possesses.  Truth  may  be  defined  to 
be  the  conformity  of  our  mental  representations  to  the 
things  which  they  are  intended  to  represent ;  and  in  Ap- 
plied Logic,  where  we  are  concerned  not  only  with  the 

*  Philosophy  of  the  Inductive  Sciences,  Vol.  I.  p.  144. 
14*  U 


322  APPLIED  LOGIC. 

Form,  but  with  the  Matter,  of  Thought,  truth  is  the  chief 
object  in  view,  —  the  first  requisite  of  Science.  The  Syn- 
thesis in  thought  is  true  only  when  it  corresponds  to  the 
combination  which  exists  in  nature. 

In  like  manner,  the  Classification  which  is  to  serve  the 
purposes  of  Science  cannot  be  arbitrary.  In  the  construc- 
tion of  Science,  the  first,  and  perhaps  the  most  difficult, 
question  which  we  have  to  answer  is,  What  classes  ought 
to  be  formed.  "  The  power  of  framing  classes,"  says  Mr. 
Mill,  "  is  unlimited,  as  long  as  there  is  any  (even  the 
smallest)  difference  to  found  a  distinction  upon.  Take 
any  attribute  whatever,  and  if  some  things  have  it  and 
others  have  it  not,  we  may  ground  upon  this  attribute  a 
division  of  all  things  into  two  classes ;  and  we  actually  do 
so,  the  moment  we  create  a  name  which  connotes  the 
attribute "  ;  —  as  the  class  of  white  things,  and  that  of 
things  not-white.  "  The  number  of  possible  classes,  there- 
fore, is  boundless ;  and  there  are  as  many  actual  classes 
(either  of  real  or  imaginary  things)  as  there  are  general 
names,  positive  and  negative  together." 

The  relations  and  connections  of  the  various  attributes 
with  each  other  must  guide  us  in  selecting  those  upon 
which  the  Classification  is  to  be  founded.  The  purpose  of 
the  arrangement  is,  that  all  the  individual  objects  included 
in  any  one  class  shall  have  as  many  common  or  similar 
elements  as  possible  ;  —  that  they  shall  resemble  each  other 
in  numerous  and  important  respects.  Now  it  is  found  that 
certain  attributes  always  carry  along  with  them,  or  are 
constantly  found  in  company  with,  many  other  attributes ; 
—  not  merely  those  which  are  necessarily  thus  connected 
as  derivative  from  them  by  necessary  inference,  but  many 
others,  of  which  we  can  only  say  that  nature  always  puts 
them  together.  On  the  other  hand,  certain  attributes 
have  no  such  regular  companionship,  but  are  found  indif- 
ferently in  connection  with  entirely  different  sets  of  ele- 


APPLIED   LOGIC.  323 

ments.  Among  inorganic  bodies,  for  example,  the  metallic 
property  is  an  instance  of  the  former  class  ;  among  animals, 
the  possession  of  a  vertebrated  column  or  backbone.  There 
is  good  reason,  then,  for  forming  a  class  of  Metals,  and  a 
class  of  Vertebrates,  because  we  are  sure  that  each  of  these 
classes  will  have  many  common  properties,  besides  the  sin- 
gle one  from  which  their  name  is  derived.  On  the  con- 
trary, the  same  color  or  the  same  magnitude  is  not  found  in 
constant  companionship  with  many  other  qualities,  so  that 
it  would  be  comparatively  useless  to  form  a  class  of  white 
objects,  or  a  class  of  animals  three  feet  high.  Such  classes 
would  be  found  to  include  the  most  dissimilar  and  hetero- 
geneous members. 

It  is  evident  even  from  these  few  examples,  that  the 
quality  selected  as  a  principle  of  Classification  Is  not  usu- 
ally an  obvious  or  conspicuous  trait.  The  casual  observer 
would  generally  think  that  it  was  small  and  insignificant. 
Thus,  the  Botanist,  disregarding  the  size,  shape,  and  color 
of  trunk,  branches,  and  leaves,  founds  an  important  classi- 
fication of  plants  upon  the  minute  and  rudimentary  cotyle- 
dons, or  seed-coverings.  All  the  Monocotyledons  are  En- 
dogens,  and  therefore  have  in  common  all  the  numerous 
traits  of  that  great  tribe  or  family ;  while  the  Dicotyledons 
are  all  Exogens.  On  the  other  hand,  the  number  and 
relative  position  of  the  stamens  and  pistils,  on  which  Lin- 
naeus founded  his  artificial  system,  are  not  found  to  be 
invariably  joined  with  any  important  features  in  the  organ- 
ization of  the  vegetable  kingdom.  It  should  be  observed, 
however,  that  classifications  are  framed  for  different  uses  ; 
and  the  peculiar  nature  of  the  purpose  in  view  may  justify 
an  arrangement  that  would  be  otherwise  indefensible. 
Thus,  the  alphabetical  order  is  the  only  convenient  one  for 
a  dictionary;  but  only  such  classifications  of  words  are 
properly  scientific  as  are  found  in  Logic  and  Grammar. 

In  02  ler  to  carry  on  the  Classification,  and  erect  a  hie- 


321  APPLIED   LOGIC. 

rarchy  of  Concepts  of  many  ascending  steps,  it  is  absolutely 
essential  that  the  Infima  Species,  or  class  first  formed, 
should  embrace  only  those  individuals  which  have,  at  least, 
several  common  attributes.  There  must  be,  at  least,  as 
many  of  these  attributes  as  will  furnish  a  Specific  Differ- 
ence for  each  step  in  the  ascending  scale. 

Passing  now  from  the  science  of  coexistent  objects  to 
that  of  events  which  succeed  one  another  in  time,  we  come 
upon  a  totally  different  principle  of  connection.  In  the 
former  case,  it  was  the  Concept  of  substance;  in  the  pres- 
ent one,  it  is  that  of  causation.  It  belongs  to  Metaphysics 
rather  than  to  Logic  to  explain  the  peculiar  nature  of  the 
relation  of  Cause  and  Effect.  Here  it  is  enough  to  say, 
that  the  connection  between  them  is  conceived  to  be  abso- 
lute or  nedfessary ;  where  the  Cause  exists,  the  Effect  must 
follow,  and  the  presence  of  the  Effect  is  inconceivable  un- 
less the  Cause  immediately  precedes  it.  But  causation,  as 
well  as  substance,  is  incognizable  through  the  perceptions  of 
sense.  In  the  outward  world,  at  least,  we  never  can  per- 
ceive the  nexus,  the  bond  of  union  which  compels  the  Effect 
to  follow.  We  believe  that  it  exists,  and  that  the  connec- 
tion is  a  necessary  one ;  but  we  are  compelled  to  infer  its 
existence  from  the  in  variableness  of  the  sequence  in  time 
between  the  two  events.  If  heat  is  applied  to  wax,  the 
wax  always  melts ;  if  poison  in  sufficient  quantity  is  taken 
into  the  stomach,  the  man  invariably  dies.  Hence  we  are 
led  to  believe  that  the  heat  causes  the  melting,  and  the 
.poison  causes  the  death ;  or,  in  other  words,  that  the  sub- 
sequent event  is  the  necessary  result  of  some  power  or  force 
in  the  antecedent,  which,  though  it  cannot  be  perceived  by 
us,  inevitably  produces  this  phenomenon.  If  heat  be  a  true 
Cause,  the  melting  of  the  wax  must  follow ;  but  as  far  as 
our  experience,  and,  if  human  testimony  may  be  believed, 
as  far  as  all  human  experience  has  gone,  the  melting  always 
does  follow;  therefore,   the  heat  is  the  Cause.     On  such 


APPLIED   LOGIC.  325 

reasoning  as  this,  all  om  evidence  of  physical  causation  — 
i.  e.  of  Causation  in  the  material  universe  —  depends.  But 
it  is  obvious  that  the  reasoning  is  illogical  and  the  evidence 
is  insufficient.  Human  experience  is  limited;  it  extends 
only  to  a  certain  number  of  cases,  —  no  matter  to  how 
many,  as  the  number  is  certainly  finite.  Any  number  of 
instances  of  actual  measurement  would  never  satisfy  the 
geometer  that  the  three  angles  of  a  triangle  must  equal  two 
right  angles.  It  is  conceivable  —  nay,  the  case  has  actu- 
ally happened  —  that,  after  one  hundred  millions  of  favor- 
able instances  occurring  in  uninterrupted  succession,  the 
hundred-million-and-first  instance  should  be  an  exception, 
or  one  of  an  opposite  character.  Mr.  Babbage  tells  us  that 
his  Calculating  Machine  may  be  so  adjusted  that,  when  put 
in  regular  motion  by  the  descent  of  a  weight,  it  will  pre- 
sent to  the  eye  successively  the  series  of  natural  numbers, 
1,  2,  3,  4,  5,  &c. ;  that,  if  we  should  have  patience  and  time 
to  watch  it  long  enough,  we  should  find  that  it  would 
present  this  series  in  one  unbroken  chain  from  1  up  to 
100,000,000,  each  term  exceeding  its  antecedent  by  unity. 
Now  an  induction  extending  successively  to  100,000,000 
terms,  without  a  single  inconformable  instance  being  dis- 
covered, would  be  regarded  by  most  persons  as  equivalent 
to  a  demonstration  that  the  law  of  the  series  was  universal 
or  absolute.  But  in  fact,  the  next  number  presented, 
after  100,000,001,  instead  of  being  100,000,002  would  be 
100,010,002,  and  the  next  term  would  be  100,030,003. 
Human  experience,  then,  as  it  is  limited  to  a  finite  number 
of  cases,  can  never  establish  an  absolute  law,  or  prove  that 
a  certain  result  is  necessary.  As  the  very  idea  of  Efficient 
Causation  involves  that  of  the  necessary  consequence  of  the 
Effect,  it  follows  that  the  range  of  human  experience  in 
the  material  universe  does  not  extend  to  the  discovery  of 
Causes  properly  so  called. 

In  all  the  Physical  Sciences,  then,  causation  should  be 


326  APPLIED  LOGIC. 

understood  to  mean  only  constant  conjunction  in  time.  We 
cannot  even  declare  that  this  conjunction  is  absolutely 
invariable;  all  that  can  be  said  is,  that  it  has  been  invari- 
able so  far  as  human  observation  has  extended,  and  we 
may  firmly  believe  that  no  instance  will  ever  be  found  to 
the  contrary.  But  this  is  not  a  necessary  belief;  its  con- 
tradictory neither  violates  any  Law  of  Thought,  nor  any  of 
the  primitive  and  ineradicable  laws  of  human  belief.  The 
assumed  invariability  of  what  are  called  "  the  laws  of  na- 
ture "  rests  upon  no  foundation  whatever  but  uniform  ex- 
perience, and  is  absolutely  certain,  therefore,  only  to  the 
extent  of  that  experience.  That  a  Law  of  Nature  may  here- 
after be  violated,  or  be  altogether  changed,  is  not  merely 
conceivable;  we  say  as  much  as  that  of  any  Judgment 
which  does  not  contradict  one  of  the  Axioms  of  Pure 
Thought.  Such  a  violation  or  change  must  be  pronounced 
to  be  possible,  though  not  probable.  Our  only  reason,  for 
instance,  for  believing  that  sugar  always  will  be  soluble  in 
water,  and  that  powdered  chalk,  under  the  same  circum- 
stances, will  always  be  insoluble,  is,  that,  though  a  vast 
number  of  experiments  have  been  tried,  we  have  not,  as 
yet,  known  or  heard  of  one  instance  to  the  contrary. 

But  in  the  strict  meaning  of  the  word  cause,  —  that  is, 
efficient  cause,  —  what  is  called  the  Law  of  Causation  is 
absolute  ;  it  is,  in  the  strictest  meaning  of  the  term,  impos- 
sible that  any  event  should  take  place  without  a  true 
Cause.  I  do  not  say  that  the  contradictory  of  this  Law 
would  violate  any  Axiom  of  Pure  Thought ;  for  as  we  are 
now  concerned,  not  with  the  Form,  but  with  the  Matter, 
of  Thought,  these  Axioms  are  inapplicable.  But  it  may 
be  said  that  the  Law  of  Causation  is  held  to  be  inviolable 
by  what  I  have  here  called  "  the  primitive  and  ineradicable 
laws  of  human  belief."  It  is,  for  instance,  just  as  impos- 
sible for  us  to  believe  that  an  event  should  take  place  with- 
out a  Cause,  as  it  is  to  believe  that  any  particular  space 


APPLIED  LOGIC.  327 

6hould  be  annihilated,  or  that  what  1  am  now  conscious  of 
does  not  really  exist  as  a  mental  phenomenon.  He  who 
can  believe  that  space  has  limits  or  boundaries  beyond 
which  there  is  no  space,  or  that  he  himself  does  not  exist 
as  a  thinking  being,  may  also  believe  that  a  physical  event 
can  take  place  without  a  Cause ;  no  sane  person  is  capable 
of  crediting  either  of  these  propositions. 

The  distinction  here  established  would  seem  to  authorize 
some  change  of  the  phraseology  usually  employed  in  Phys- 
ical Science.  What  has  hitherto  been  denominated,  not 
only  by  physicists,  but  by  people  generally,  a  cause,  might 
more  properly  be  called  a  constant  condition,  of  the  phe- 
nomenon. What  the  physical  inquirer  is  really  in  search  of, 
when  he  is  inquiring  after  what  he  calls  the  cause  of  any 
event,  is  a  constant  antecedent  of  it,  which,  being  discovered, 
will  ever  afterwards  enable  him,  should  not  the  sequence 
of  antecedent  and  consequent  be  altered,  (and  of  this  he 
justly  entertains  no  fears  whatever,)  to  predict  the  recur- 
rence of  the  phenomenon.  To  him,  the  Law  of  Causa- 
tion, to  adopt  Mr.  J.  S.  Mill's  language,  means  only  this: 
u  For  every  event,  there  exists  some  combination  of  events, 
some  given  concurrence  of  circumstances,  positive  and  neg- 
ative, the  occurrence  of  which  will  always  be  followed  by 
that  phenomenon."  Under  this  view,  the  so-called  Laws 
of  Nature  might  more  properly  be  denominated  General 
Facts,  as  the  word  "  law  "  generally  implies  what  is  abso- 
lute or  necessary.  But  as  any  sweeping  change  of  scien- 
tific phraseology  is  hardly  to  be  expected,  the  language 
heretofore  in  use  must  continue  to  be  employed,  though 
under  protest  from  those  who  understand  the  impropriety 
of  its  application.  There  may  be  Laws  of  Nature  which 
are  absolutely  invariable ;  but  it  is  certain  that  none  such 
have  been,  or  ever  can  be,  discovered.  Human  science  is 
merely  able  to  establish  certain  General  Facts,  which  are 
indisputably  true  only  to  the  extent  of  our  experience. 


328  APPLIED   LOGIC. 

"We  shall  hereafter  examine  some  of  the  reasons  which 
have  caused  a  higher  degree  of  certainty  and  generality 
to  be  attributed  to  these  Facts  than  they  actually  deserve. 

It  is  manifest-  from  what  has  been  said,  that  Science  is 
made  up  of  two  sorts  of  cognitions,  —  those  in  which  the 
objects  are  given  as  contingent  phenomena,  and  those  in 
which  the  objects  are  given  as  necessary  facts  or  laws 
The  former  are  called  empirical,  as  they  are  derived  fron? 
experience,  and  are  true  only  to  the  extent  of  that  experi- 
ence. Their  origin  is  also  said  to  be  a  posteriori,  because 
they  are  subsequent  to  experience.  The  latter  are  said  to 
be  a  priori  in  origin,  for  although  first  manifested  on  occa- 
sion of  experience,  they  are  truly  prior  to  it ;  for  if  they 
had  not  previously  existed,  as  native  to  the  mind  and  in- 
wrought into  its  very  constitution,  experience  itself  would 
not  have  been  possible.  We  have  already  had  examples 
of  such,  in  our  notions  of  substance,  cause,  space,  time,  &c. 
These  may  be  expressed,  as  here,  each  by  a  single  term 
which  is  significant  of  one  act  of  the  mind,  —  an  indivisible 
Intuition  or  Thought;  or  they  may  be  resolved  into  one 
or  more  Judgments,  as  statements  of  necessary  laws.  Thus, 
the  cognition  of  substance  may  be  resolved  into  this  Law, 
that  every  real  attribute  or  quality  presupposes  some  sub- 
stance in  which  it  inheres.  Cause,  as  already  mentioned, 
furnishes  the  universal  and  absolute  Law  of  Causation,  that 
every  physical  event  or  change  must  have  a  cause.  The  In- 
tuition of  space  yields  many  necessary  Judgments,  thus: 
Every  physical  object  must  exist  in  space  ;  Space  is  inde- 
structible, even  in  Thought,  as  a  whole,  or  in  any  of  its  parts; 
Space  is  boundless ;  &c.  The  notion  of  Time  also  is  re- 
solved into  several  necessary  laws,  thus  :  Every  event  must 
take  place  at  some  determinate  point  in  time  ;  Time  necessa- 
rily flows  on  in  one  continuous  lapse ;  Time  is  boundless 
both  before  and  after,  or,  as  the  Schoolmen  say,  both  a 
parte  ante  and  a  parte  post ;  &c. 


APPLIED  LOGIC.  329 

These  necessary  Laws  must  be  regarded  as  mere  ex- 
plications of  their  respective  a  priori  cognitions ;  they  are 
not  inferences  from  such  cognitions,  but  are  involved  in 
them,  so  that  it  is  impossible  to  have  a  full  and  adequate 
conception  of  the  one  —  that  is,  to  fully  understand  the 
meaning  of  the  term  —  without  the  other.  In  neither 
form,  as  one  conception  nor  as  a  judgment,  can  they  be  de- 
rived from  experience  ;  for  experience  can  only  tell  me  of 
what  is  true  in  certain  cases,  —  namely,  those  cases  which 
I  or  other  persons  have  actually  witnessed;  while  these 
Laws  are  known  to  be  absolutely  true  for  all  cases  past, 
present,  and  future.  All  the  maxims  of  experience  are 
reversible  in  thought;  that  is,  I  can  conceive  that  their 
opposites  or  contraries  should  be  true ;  —  I  can  conceive, 
for  instance,  that  fire  should  not  burn,  that  water  should 
not  drown,  that  stones  should  fall  upwards  instead  of  down- 
wards, that  "  when  the  brains  were  out,  the  man  should 
not  die."  But  these  necessary  cognitions  a  priori  are  not 
reversible  in  thought ;  I  cannot  conceive  that  an  attribute 
should  exist  without  a  substance,  or  that  space  should  be 
annihilated,  or  have  limits  affixed  to  it,  or  that  a  physical 
event  should  take  place  without  a  Cause.  Moreover,  as 
has  been  said,  these  cognitions  are  prerequisites  of  experi- 
ence, without  which  experience  itself  would  not  be  possible. 
As  no  body  can  exist  without  space,  no  quality  without  a 
substance,  I  could  not  have  my  first  experience  of  either, 
—  that  is,  I  could  not  know  body  to  be  body,  or  qua  ity  to 
be  quality,  —  unless  these  cognitions  were  already  present 
to  the  mind,  although  then  first  drawn  out  and  made  dis- 
tinct to  consciousness.  As  the  capacity  of  being  exploded 
must  be  conceived  to  exist  in  the  gunpowder  before  the 
actual  explosion  can  take  place,  although  this  capacity  was 
latent  up  to  that  moment,  so  the  cognition  of  space  must 
have  been  in  the  mind  before  we  could  have  a  conception 
of  body,  and  the  cognition  of  time,  before  we  could  have 
that  of  an  event,  since^  every  event  must  be  in  time. 


330  APPLIED   LOGIC. 

And  yet  these  cognitions  are  not,  like  the  Axioms  which 
we  formerly  considered,  mere  Laws  of  thought ;  for  they  are 
necessarily  apprehended  as  actual  and  immutable  Laws  of 
real  things.  It  is  true,  that  the  attribution  of  these  Laws  to 
actual  phenomena  is  an  act  of  thought ;  so  is  all  cognition, 
whether  of  external  events  and  things,  or  of  abstract  uni- 
versal principles.  Berkeley  and  other  Idealists,  then,  who 
hold  that  what  we  call  external  realities  exist  only  in 
the  mind,  may  consistently  maintain  that  these  a  priori 
cognitions  are  merely  necessities  of  thinking  thus  and  so. 
But  the  Realist,  who  believes  in  the  objective  validity  of 
our  external  perceptions,  who  holds  that  things  are  what 
they  seem  to  be,  cannot  consistently  deny  the  objective 
reality  of  those  Forms  and  Laws  without  which  any  external 
existence  would  be  impossible,  —  which  are,  in  fact,  neces- 
sary conditions  of  the  reality  of  such  existence.  Hence  I 
cannot  but  regard  Kant's  elaborate  attempt  to  reduce  these 
cognitions  to  mere  Laws  of  Thought  as  inconsistent  with  his 
own  doctrine.  He  affirms  that  we  have  no  knowledge  of 
external  realities,  and  are,  therefore,  incompetent  to  pro- 
nounce whether  they  do,  or  do  not,  possess  certain  attri- 
butes ;  and  yet  he  declares  that  "  things  in  themselves  " 
have  a  real  existence  apart  from  our  thoughts.  He  admits 
the  distinction  between  noumena  and  phenomena,  between 
things  as  they  are  and  things  as  they  appear,  and  asserts 
the  reality  of  the  former,  though  they  are  wholly  incogniza- 
ble to  our  minds.  But  if  they  are  absolutely  incognizable, 
how  does  he  know  that  they  do  not  exist  under  the  Laws  of 
space,  time,  and  Cause ;  and  if  they  are  real,  how  can  they 
exist  except  under  those  Laws  which  are  the  conditions  of 
all  reality  ?  To  deny  the  objective  validity  of  these  Laws 
is  to  contradict  the  primitive  testimony  of.  consciousness, 
and  to  cut  away  the  foundations  of  all  philosophy,  whether 
dogmatic,  critical,  or  sceptical,  by  impeaching  the  correct- 
ness, of  those  principles  and  arguments  by  which  the  sceptic 


APPLIED  LOGIC.  331 

himself  attempts  to  show  the  reasonableness  of  his  doubts. 
I  have  no  better  and  no  other  reason  for  affirming  that  two 
straight  lines  cannot  enclose  a  space,  than  for  pronouncing 
that  space  itself  exists  in  some  other  manner  than  as  a 
mere  law  of  the  perceptive  faculty.  The  doctrine  of  the 
Idealists  is  at  least  intelligible ;  for  I  can  imagine  the  an- 
nihilation or  non-existence  of  objects  in  space ;  but  the 
non-existence  of  space  itself  is  literally  unthinkable.  It  is 
a  mere  paradox  to  assert  the  reality  of  the  objects,  whose 
existence  is  contingent,  and  deny  that  of  space,  which 
exists  by  necessity.  And  the  argument  is  worse  than  the 
doctrine  which  it  is  offered  to  support ;  since  the  only  rea- 
son alleged  for  believing  space  and  time  to  be  unreal,  is  the 
impossibility  of  thinking  that  they  are  unreal. 

In  conformity  with  what  has  been  said,  it  might  seem 
that  the  doctrine  of  the  formation  of  Science  would  prop- 
erly fall  into  two  great  divisions ;  the  one  relating  to  the 
acquisition  of  contingent  knowledge  by  means  of  expe- 
rience, and  the  other  to  the  attainment  of  necessary 
knowledge  by  the  development  and  application  of  those 
primitive  truths  which  are  revealed  to  us  in  the  very  con- 
stitution of  our  minds.  And,  in  a  certain  sense,  this  divis- 
ion exists.  Geometry  and  Arithmetic,  as  the  sciences  of 
continuous  and  discrete  quantity,  are  applied  most  directly, 
and  in  their  purest  form,  to  the  conceptions  of  space  and 
time,  in  which  these  two  modes  of  quantity  are  most 
clearly  manifested,  not  being  modified  or  confused  by  the 
presence  of  other  attributes.  The  lapse  of  time  cannot  be 
conceived  or  expressed  except  by  the  idea  of  number,  or 
discrete  quantity ;  and  the  extent  of  space,  in  like  manner, 
is  necessarily  conceived  as  continuous  quantity.  And  in 
both  cases,  our  conception  of  pure  quantity  is  most  distinct, 
because  there  are  so  few  other  attributes  of  space  and  time 
with  which  it  might  become  confused.  But  these  two 
sciences  are   not   restricted   to   the   consideration  of  pure 


332  APPLIED  LOGIC. 

space  and  time,  and  do  not  exhaust  our  conceptions  of 
them.  They  relate  to  space  and  time  only  so  far  as 
these  are  magnitudes,  or  things  to  be  measured ;  and  they 
relate  to  everything  else,  so  far  forth  as  any  other  thing  is 
susceptible  of  measurement.  Mathematics  itself  is  the 
science  of  relative  magnitude.  Thus,  Algebra,  which  is 
the  highest  form  of  mathematical  generalization,  is  the 
science  of  pure  magnitude,  or  quantity  in  the  abstract,  and 
thus  includes  both  Geometiy  and  Arithmetic,  since  its 
principles  and  formulas  are  alike  and  indiscriminately  ap- 
plicable both  to  space  and  time.  Thus  the  expression  for 
the  square  of  the  sum  of  two  quantities,  (a  -\-  5)2  =  a2  + 
2ab  -f-  b2,  holds  true  alike  for  continuous  and  discrete 
quantity,  for  space  and  time  ;  since  it  is  equally  an  expres- 
sion of  the  truth,  that  the  square  erected  upon  the  sum  of 
two  lines  may  always  be  resolved  into  two  smaller  squares 
and  two  rectangles,  corresponding  to  the  formula ;  and  also 
of  that  which  is  only  another  aspect  of  the  same  truth, 
viz.  that  the  arithmetical  expression  for  the  square  of  the 
sum  of  two  numbers  may  be  resolved  in  precisely  the  same 
manner. 

It  does  not  appear,  then,  that  what  are  called  the  de- 
monstrative sciences  owe  their  attribute  of  logical  certainty 
to  the  peculiar  nature  of  the  subjects  about  which  they  are 
conversant.  It  is  not  because  space  and  time  are  at  once 
necessary  conceptions  of  the  intellect  and  immutable  laws 
of  real  things,  that  the  mathematician  is  able  to  build  up 
his  vast  fabric  of  pure  truths,  which  are  absolutely  certain 
and  are  independent  of  any  verification  by  experience. 
The  science  of  pure  quantity,  which  seems  to  me  the  only 
proper  definition  of  mathematics,  is  also  the  science  of  real 
things,  but  so  far  only  as  these  are  affected  by  quantity 
and  thus  subject  to  measurement,  and  so  far  only  as  this 
measurement  is  executed  with  that  ideal  precision  and 
accuracy  which   are   presupposed   in   every  mathematical 


APPLIED  LOGIC.  333 

investigation.  The  necessary  and  a  priori  cognitions  of 
the  human  mind  do  not  constitute  a  department  of  science 
by  themselves,  but  are  interwoven  with  the  empirical  ele- 
ments of  our  knowledge.  Their  office  is  not  constitutive, 
but  regulative.  They  determine  the  limits  of  the  under- 
standing, prescribe  its  functions,  and  regulate  its  belief. 
Whatever  is  apprehended  under  the  relations  of  Quantity, 
is  subject  to  the  immutable  laws  of  Quantity.  Whatever  is 
known  as  an  event  or  change,  is  governed  by  the  necessary 
laws  of  Causality  and  Time.  Attributes  or  qualities  are 
apprehended  under  the  law  of  Substance,  which  determines 
the  mode  of  their  existence.  It  is  only  by  abstraction,  or 
disjoining  in  thought  what  cannot  be  separated  in  reality, 
that  a  separate  science  can  be  created  of  necessary  cog- 
nitions a  priori,  as  in  that  branch  of  Metaphysics  which  is 
called  Ontology. 

Going  back  to  the  physicist's  conception  of  Cause,  that 
is,  Invariable  Antecedence,  we  observe  that  the  method  of 
distinguishing  invariable  sequences  from  accidental  ones  is 
by  analysis.  Every  event  has  many  antecedents  and  a 
crowd  of  concomitant  circumstances.  We  seek  to  ascertain 
which  of  these  are  necessary  conditions  of  the  phenomenon 
by  analyzing  them  ;  that  is,  by  trying  the  experiment  over 
again,  leaving  out  each  time  one  or  more  of  the  attendant 
circumstances  ;  if  the  same  result  still  follows,  the  circum- 
stances thus  left  out  are  not  the  causes  which  we  are  in 
search  of,  but  were  only  accidental  concomitants,  that  did 
not  at  all  affect  the  issue.  Proceeding  in  this  manner, 
step  by  step,  we  come  at  last  to  some  of  the  original  ante- 
cedents, which  being  omitted,  the  event  no  longer  takes 
place.  Then,  in  common  parlance,  we  are  said  to  have 
discovered  the  cause  of  the  phenomenon ;  strictly  speak- 
ing, it  is  only,  so  far  as  we  know,  its  invariable  antecedent, 
or  a  condition  of  its  existence,  —  perhaps  only  a  condition 
of  our  knowing  that  it  exists.     The  whole  method  is  ten- 


334  APPLIED   LOGIC. 

tative,  and  is  evidently  exposed  to  error,  as  it  is  only  an 
application  of  that  fallacious  mode  of  reasoning  which  has 
been  exposed  as  the  sophism  post  hoc,  ergo  propter  hoc. 
Hence,  the  conclusion  is  not  held  to  be  established  for  the 
purposes  of  science,  until  the  experiment  has  been  tried,  or 
the  observation  repeated,  under  every  possible  variety  of 
circumstances.  But  a  large  experience,  especially  if  con- 
firmed by  some  analogy  between  this  phenomenon  and 
others  that  are  known  to  follow  similar  antecedents,  may 
establish  the  conclusion  beyond  all  reasonable  doubt. 

As  our  knowledge  of  the  phenomena  of  succession  in- 
creases, the  Concepts  which  we  form  of  individual  objects 
and  classes  of  objects  become  larger  and  more  complex. 
Our  conception  of  any  corporeal  thing  must  include  not 
only  those  obvious  qualities,  such  as  shape,  color,  specific 
gravity,  texture,  &c,  which  it  manifests  on  nearly  all 
occasions,  but  the  changes  to  which  these  are  subject  when 
it  is  brought  in  contact  with  other  substances  under  differ- 
ent circumstances,  and  also  those  changes  in  other  bodies 
of  which  its  presence  may  be  a  constant  antecedent. 
"  The  ideas,"  says  John  Locke,  "  that  make  up  our  com- 
plex notions  of  corporeal  substances  are  of  these  three 
sorts.  First,  the  ideas  of  the  primary  qualities  of  things, 
which  are  discovered  by  our  senses,  and  are  in  them  even 
when  we  perceive  them  not ;  such  are  the  bulk,  figure, 
number,  situation,  and  motions  of  the  parts  of  bodies,  which 
are  really  in  them,  whether  we  take  notice  of  them  or  no. 
Secondly,  the  sensible  secondary  qualities,  which,  depend- 
ing on  these,  are  nothing  but  the  powers  those  substances 
have  to  produce  several  ideas  in  us  by  our  senses  ;  which 
ideas  are  not  in  the  things  themselves,  otherwise  than  as 
anything  is  in  its  Cause.  Thirdly,  the  aptness  we  consider 
in  any  substance  to  give  or  receive  such  alterations  of 
primary  qualities  as  that  the  substance  so  altered  should 
produce  in  us  different  ideas  from  what  it  did  before ;  these 


APPLIED  LOGIC.  335 

are  called  active  and  passive  powers  ;  all  which  powers,  so 
far  as  we  have  any  notice  or  notion  of  them,  terminate 
only  in  sensible  simple  ideas.  For  whatever  alteration  a 
loadstone  has  the  power  to  make  in  the  minute  particles  of 
iron,  we  should  have  no  notion  of  any  power  it  had  at  all 
to  operate  on  iron,  did  not  its  sensible  motion  discover  it ; 
and  I  doubt  not  but  there  are  a  thousand  changes,  that 
bodies  we  daily  handle  have  a  power  to  cause  in  one 
another,  which  we  never  suspect,  because  they  never  ap- 
pear in  sensible  effects." 

"  Powers  therefore  justly  make  a  great  part  of  our  com 
plex  ideas  of  substances.  He  that  will  examine  his  com 
plex  idea  of  gold,  will  find  several  of  its  ideas  that  make  it 
up  to  be  only  powers ;  as  the  power  of  being  melted,  but 
of  not  spending  itself  in  the  fire,  of  being  dissolved  in  aqua 
regia,  are  ideas  as  necessary  to  make  up  our  complex  idea 
of  gold,  as  its  color  and  weight ;  which,  if  duly  considered, 
are  also  nothing  but  different  powers.  For  to  speak  truly, 
yellowness  is  not  actually  in  gold,  but  is  a  power  in  gold 
to  produce  that  idea  in  us  by  our  eyes,  when  placed  in  a 
due  light ;  and  the  heat  which  we  cannot  leaVe  out  of  our 
idea  of  the  sun  is  no  more  really  in  the  sun,  than  the 
white  color  it  introduces  into  wax.  These  are  both  equally 
powers  in  the  sun,  operating,  by  the  motion  and  figure  of 
its  sensible  parts,  so  on  a  man,  as  to  make  him  have  the 
idea  of  heat,  and  so  on  wax,  as  to  make  it  capable  to  pro- 
duce in  a  man  the  idea  of  white."  * 

A  fourth  class  of  the  elements  that  form  our  Concepts  of 
individual  objects  consists  of  the  Relations  in  which  these 
objects  stand  to  other  things.  These,  of  course,  are  num- 
berless, and  therefore  are  a  great  source  of  the  indistinctness 
and  imperfection  of  this  sort  of  knowledge.  Every  object 
may  be  compared  with  every  other  object  in  nature,  and 
with  every  Concept  which  the  mind  has  previously  formed ; 

•  Essay  on  Human  Understanding,  Book  II.  Chap.  23,  §§  9  and  10. 


336  APPLIED   LOGIC. 

and  of  the  countless  Relations  thus  brought  to  our  notice, 
many  are  essential  to  an  adequate  knowledge  of  the  related 
object.  Most  of  Aristotle's  Categories  are  an  imperfect 
attempt  to  classify  these  Relations,  and  place  them  under 
their  summa  genera.  Some  of  them,  such  as  those  of 
Quantity,  Place,  and  Time,  are  definite  and  admit  of  accu- 
rate determination ;  as  such,  they  are  the  objects  of  the 
Exact  Sciences.  Others,  like  those  of  Quality,  Posture, 
and  Modes  of  Being,  Doing,  and  Suffering,  are  wholly 
indeterminate,  at  least  in  this  respect,  that  their  various 
sorts  and  degrees  are  shaded  into  each  other  imperceptibly, 
or  without  any  natural  lines  of  demarcation.  These,  of 
course,  can  be  grouped  into  classes  only  in  some  rough 
and  arbitrary  way,  the  divisions  not  being  marked  out  by 
nature.  As  our  knowledge  of  them  is  thus  vague  and 
incomplete,  our  conclusions  or  inferences  concerning  them 
must  be  uncertain,  and  the  Sciences  under  which  they  fall 
may  be  said  to  be  occupied  with  Contingent  Matter. 

In  Applied  Logic,  the  test  of  the  adequacy  of  a  Concept 
is  its  more  or  less  complete  enumeration  of  the  essential 
qualities  of  the  real  thing,  or  class  of  things,  which  it  de- 
notes. Any  attempt  to  ascertain  and  enumerate  all  of 
these  empirically,  or  by  successive  observations  and  experi- 
ments, is  hopeless ;  a  lifetime  would  not  suffice  to  accumu- 
late more  than  a  small  fraction  of  such  knowledge  of  a 
single  object.  Thus,  its  active  and  passive  powers,  as 
they  are  termed,  or,  more  properly,  the  fixed  Relations  of 
antecedence  and  consequence  which  subsist  between  the 
changes  affecting  it  and  those  affecting  all  other  substances, 
could  be  ascertained  only  by  placing  it  in  juxtaposition  with 
every  other  thing  singly,  and  with  every  conceivable  com- 
bination of  other  things.  Apply  heat  or  water  to  some  one 
substance  taken  separately,  and  only  two  or  three  series  of 
changes  would  be  observed,  such  as  its  greater  or  less  fusi- 
Vlity,  solubility,  absorption  of  heat  or  fluid,  capability  of 


APPLIED   LOGIC.  337 

being  oxidized,  &c.  But  apply  the  same  agents  to  it  in 
combination  with  one  or  more  other  substances,  and  series 
of  very  different  phenomena  may  be  manifested.  By  rea- 
son of  the  endless  number  and  variety  of  such  possible 
observations  and  experiments,  the  results  of  them  in  a  vast 
majority  of  cases  being  individual  truths  of  no  special  inter- 
est or  importance,  no  one  can  think  of  engaging  in  them  by 
detail,  or  with  a  view  of  exhausting  the  round  of  possible 
inquiry  and  trial ;  and  hence  our  knowledge  must  always 
fail  infinitely  short  of  the  truth  of  things.  The  most  im- 
portant single  facts  of  this  character  now  known  to  man 
were  accidentally  discovered ;  they  are  the  fruits,  not  of 
study  and  research,  but  of  mere  chance.  Hence  we  sel- 
dom know  the  history  of  such  discoveries,  or  the  person 
who  made  them.  Centuries  after  the  attractive  power  of 
magnetic  iron  had  been  known,  some  one,  we  know  not 
who,  happened  to  observe  its  polarity,  or  quality  of  point- 
ing constantly  to  the  north ;  and  the  result  was  the  inven- 
tion of  the  mariner's  compass.  The  ancients  were  familiar 
with  the  obvious  qualities  of  nitre,  sulphur,  and  charcoal ; 
but  some  obscure  alchemist,  some  time  in  the  fourteenth 
century,  happened  to  mix  them  together  in  the  right  pro- 
portions, and  the  explosion  which  ensued  taught  the  world 
the  secret  of  gunpowder.  The  art  of  printing  was  hit 
upon  by  a  similar  lucky  chance.  Yet  "  these  three  things," 
says  Lord  Bacon,  "  to  wit,  Printing,  Gunpowder,  and  the 
Mariner's  Compass,  have  changed  the  whole  face  and  state 
of  things  throughout  the  world ;  the  first  in  literature,  the 
second  in  warfare,  the  third  in  navigation ;  whence  have 
followed  innumerable  changes ;  insomuch  that  no  empire, 
no  sect,  no  star,  seems  to  have  exerted  greater  power  and 
influence  in  human  affairs  than  these  mechanical  discov- 
eries." 

But  as  much  the  greater  number  of  casual  observations 
of  individual  things  reveal  only  unimportant  relations  and 

15  v 


338  APPLIED  LOGIC. 

qualities,  there  is  no  encouragement  to  pursue  and  record 
them  methodically,  in  the  hope  of  hitting  at  last  upon 
some  one  of  interest  and  value.  Yet  Lord  Bacon,  misled 
by  a  few  brilliant  examples,  such  as  those  just  cited,  seems 
to  have  required,  as  the  first  step  towards  carrying  out  his 
new  system  of  inductive  research,  a  u  Natural  and  Experi- 
mental History,  sufficient  and  good,  as  the  foundation  of 
all."  This  "  History  "  was  to  be  a  complete  record  of 
individual  observations  and  experiments,  omitting  nothing 
on  account  of  its  seeming  triviality  and  obviousness,  to  be 
subsequently  digested  into  "  Tables  and  Arrangements  of 
Instances,  in  such  method  and  order  that  the  understand- 
ing may  be  able  to  deal  with  them."  *  Upon  this  vast 
store  of  crude  material,  towards  furnishing  which  he  him- 
self made  a  respectable  beginning  in  his  Historia  Naturalis 
et  Experimentalis  ad  condendam  Philosophiam,  and  his  Syl- 
va  Sylvarum,  or  a  Natural  History,  all  the  subsequent  pro- 
cesses of  his  Inductive  Method  were  to  be  expended. 
"  Since  there  is  so  great  a  number  and  army  of  particu- 
lars," he  observes,  "  and  that  army  so  scattered  and  dis- 
persed as  to  distract  and  confound  the  understanding,  little 
is  to  be  hoped  for  from  the  skirmishings  and  slight  attacks 
and  desultory  movements  of  the  intellect,  unless  all  the 
particulars  which  pertain  to  the  subject  of  inquiry  shall, 
by  means  of  Tables  of  Discovery,  apt,  well  arranged,  and 
as  it  were  animate,  be  drawn  up  and  marshalled ;  and  the 
mind  be  set  to  work  upon  the  helps  duly  prepared  and 
digested  which  these  Tables  supply."  f 

Bacon  failed  to  observe  that  the  minds  of  all  men  natu- 
rally and  inevitably  proceed  in  great  part  by  this  method,  as 
is  evinced  by  the  construction  of  language.  As  we  have 
seen,  all  words  properly  so  called  are  only  the  General 
Names  of  the  groups  and  classes  into  which  we  marshal 
<md   digest   our   individual  observations  ;  —  yet  with  this 

*  Novum  Organon,  Book  II.  Aph.  x.  f  Id.  Book  I.  Aph.  cii. 


APPLIED   LOGIC.  339 

improvement  upon  the  system  that  Bacon  recommends, 
that  the  Concepts  thus  framed  include  only  the  original 
and  essential  attributes,  the  others  being  left  out  as  of  no 
account,  and  needlessly  burdening  the  memory  by  their 
vast  number.  If  experiment  or  casual  observation  should 
hereafter  determine  that  one  of  these  omitted  elements  is 
really  of  interest  and  importance,  it  will  then  henceforward 
constitute  an  integral  part  of  the  Concept.  Every  one's 
notion  of  the  magnet  now  includes  its  attribute  of  polarity. 

Derivative  attributes,  it  has  been  mentioned,  are  not 
expressly  included  in  the  Intension  of  a  Concept,  because 
they  are  implied  and  virtually  contained  in  their  primaries. 
Thus,  the  numberless  properties  of  every  geometric  figure 
are  reduced,  in  the  Concept  which  bears  the  Name  of  that 
figure,  to  the  two  or  three  qualities,  constituting  its  Defini- 
tion, from  which  they  may  all  be  derived  by  necessary  infer- 
ence a  priori,  or  without  the  aid  of  actual  observation  and 
experiment.  Down  to  the  time  of  the  Baconian  reform  in 
the  processes  of  physical  science,  it  seems  to  have  been 
imagined  that  individual  substances  or  bodies,  like  geo- 
metric figures,  had  each  its  one  or  two  essential  properties, 
which  being  known,  all  the  others  could  be  immediately 
deduced  from  them  by  a  purely  logical  process,  without 
any  aid  from  experience.  This,  in  fact,  was  the  meaning  of 
the  word  essence,  that  internal  constitution  of  a  body  which 
makes  it  what  it  is,  or  from  winch  all  its  attributes  neces- 
sarily flow.  Change  the  essence  of  the  body,  then,  and  you 
thereby  change  all  its  properties.  To  the  eye  of  Omni- 
science, doubtless,  there  is  such  an  essence  ;  but  it  must 
ever  remain  unknown  to  man's  finite  capacities,  on  account 
of  the  endless  number  of  unknown  attributes  with  which 
it  is  intermingled.  Those  qualities  alone  appear  to  us 
essential  which  are  known  to  be  constantly  associated  with 
a  few  others,  either  because  these  others  can  be  deduced 
from  them  by  necessary  inference,  or  because  they  have 


340  APPLIED  LOGIC. 

always  been  found  together  in  a  large  experience.  In  the 
latter  case,  of  course,  the  conclusion  is  contingent  or  un- 
certain, being  necessarily  true  only  to  the  extent  of  our 
previous  observation.  In  the  former  case,  the  conclusion 
is  absolute,  if,  by  the  hypothesis,  all  other  qualities  are 
excluded  from  the  Concept  except  those  which  are  cer- 
tainly known.  In  geometry,  for  instance,  the  Concept  or 
definition  of  any  solid  body  includes  only  its  shape  and 
magnitude,  and  supposes  that  these  are  accurately  deter- 
mined ;  abstraction  is  made  of  all  its  other  qualities,  be- 
cause these  are  not  susceptible  of  perfect  determination, 
and  we  know  only  from  experience  how  far  they  associated 
with  each  other. 

If  the  Matter  of  Thought,  then,  includes  real  existences, 
or  such  objects  and  events  as  are  actually  presented  to  us 
in  nature,  our  conclusions  respecting  them,  being  derived 
only  from  experience,  must  always  be  subject  to  doubt. 
As  we  know  them  only  imperfectly,  our  inferences  respect- 
ing them  can  never  be  logically  certain.  But  if  the  Con- 
cepts are  limited  to  imaginary  objects,  consisting  only  of  a 
few  perfectly  determinate  qualities,  our  conclusions  respect- 
ing them  will  be  absolute,  though  they  will  be  applicable 
only  in  the  realm  of  pure  abstractions.  Bacon  was  right, 
then,  in  maintaining  that  the  Physical  Sciences,  so  far  as 
they  extend  to  the  knowledge  of  real  objects,  are  dependent 
solely  upon  observation  and  experiment.  "  Man,  being 
the  servant  and  interpreter  of  Nature,  can  do  and  under- 
stand so  much  only  as  he  has  observed,  either  in  fact  or  in 
thought,  of  the  course  of  Nature ;  beyond  this,  he  cannot 
understand  or  do  anything." 

We  can  now  see  what  are  the  preliminary  classifications 
upon  the  formation  of  which  all  Science  depends,  and  can 
point  out  the  principles  which  regulate  this  formation. 

1.  We  form  classes  of  real  things  or  Natural  Objects, 
arranging  them  according  to  the  similarity  of  their  attri- 


APPLIED  LOGIC.  341 

butes,  and  selecting  by  preference,  as  the  basis  of  the  clas- 
sification, those  qualities  which  are  invariably  found  con- 
joined with  the  greatest  number  of  other  uniform  qualities ; 
as  the  presence  of  one  of  these  constant  elements  enables 
us  to  infer,  in  anticipation  of  experience,  that  it  will  be 
found  in  conjunction  with  those  others.  The  science  of 
Natural  History,  in  its  various  departments,  consists  exclu- 
sively of  such  classifications,  together  with  such  descriptions 
and  definitions  as  are  subsidiary  to  them. 

2.  We  classify  the  qualities  themselves,  according  to 
their  similarities,  irrespective  of  the  real  objects  in  which 
they  inhere.  Thus,  we  form  classes  of  colors,  sounds, 
shape,  and  dimension,  degrees  of  consistency,  specific  grav- 
ity, &c.  Sometimes  a  single  set  of  these  arrangements  is 
found  important  enough  to  be  made  the  basis  of  a  distinct 
science,  as  in  the  case  of  Acoustics  and  Optics ;  more  fre- 
quently, several  sets  of  them  are  grouped  together  for 
scientific  consideration,  as  is  the  case  with  the  chemical 
qualities  of  substances. 

3.  We  classify  events  according  to  the  uniformity  of 
their  succession  in  time.  These,  if  regarded  as  mere  se- 
quences of  phenomena,  may  be  referred  to  the  subsequent 
head  of  Relations  ;  if  regarded  as  the  active  or  passive 
powers  of  bodies,  they  may  be  placed  under  the  preceding 
head  of  Qualities.  A  constant  order  of  succession  is  often 
erroneously  supposed  to  be  a  necessary  sequence,  because 
the  mind  superadds  in  such  cases  its  pure  conception  of  the 
necessary  relations  of  Cause  and  Effect ;  and  hence  sciences 
based  upon  such  classifications  are  improperly  termed 
sciences  of  causation.  Several  departments  of  Physics, 
such  as  the  sciences  of  Mechanics  and  Hydrostatics,  and 
some  divisions  of  the  moral  sciences,  such  as  Politics  and 
Civil  History,  are  made  up  chiefly  of  classifications  of  this 
sort. 

4.  We  classify  the  relations  of  things,  irrespective  of  the 


842  APPLIED   LOGIC. 

other  Qualities  and  differences  of  the  things  related.  Thus, 
Geography  is,  in  the  main,  a  classification  of  the  Relations 
of  the  different  portions  of  the  earth's  surface  to  each  other ; 
Astronomy  takes  a  similar  view  of  the  Relations  between 
the  different  members  of  the  solar  and  stellar  systems.  A 
large  portion  of  the  sciences  of  Law  and  Politics  has  regard 
to  the  different  Relations  which  subsist  between  human 
beings,  such  as  those  of  husband  and  wife,  parent  and 
child,  rulers  and  subjects,  countrymen  and  aliens,  &c. 
The  mind  takes  special  cognizance  only  of  a  very  few  of 
the  countless  Relations  which  comparison  and  reflection 
bring  to  light.  We  select  those  only  which  happen  to  be 
of  special  interest  to  us,  through  the  guidance  which  they 
afford  for  our  future  conduct,  the  wonder  and  curiosity 
which  they  excite,  or  the  bearing  which  they  may  have  in 
any  way  upon  our  welfare. 

It  is  not  meant  that  each  one  of  the  Classes  and  Sciences 
which  we  form  consists  exclusively  of  one  or  the  other  of 
the  four  species  here  enumerated.  Indeed,  the  division 
itself  is  a  very  imperfect  one,  for  the  Dividing  Members, 
as  we  have  intimated,  do  not  exclude  each  other ;  a  Con- 
cept of  Real  Things  includes  a  view  of  their  Qualities,  their 
active  and  passive  Powers,  and  their  Relations  ;  and  the 
two  latter  may  be  comprised  under  the  name  of  Qualities. 
But  these  four,  sometimes  separately  and  sometimes  in 
combination,  are  the  elements  which  we  group  together 
into  classes,  out  of  which  those  higher  classes,  or  hierar- 
chies of  Concepts,  which  we  call  Sciences,  are  subsequently 
erected.  In  every  case,  the  classifying  principle  is  simi- 
larity, or  uniformity  of  succession,  those  Objects  and  Quali- 
ties being  united  which  resemble  each  other  in  certain 
respects,  and  those  events  being  reduced  to  the  same  head 
which  uniformly  follow  one  another  under  similar  circum- 
stances. The  education  of  every  human  being  consists  in 
the  gradual  acquisition  of  a  large  stock  of  thesp  elementary 


APPLIED   LOGIC.  343 

Concepts,  which  are  taught  to  him  in  learning  the  use  of 
his  mother-tongue,  while  exercising  at  the  same  time  his 
powers  of  observation  and  reflection. 

The  advancement  of  Science  depends  on  the  success  of 
the  attempts  which  man  is  constantly  making  to  enlarge 
and  improve  the  classifications  which  are  the  bases  of  these 
Concepts.  By  detecting  hitherto  unobserved  similarities 
and  conjunctions  in  time,  we  extend  the  generalizations 
and  reduce  the  number  of  classes,  thereby  bringing  the 
infinitude  of  objects  and  events  which  nature  offers  us 
more  nearly  within  the  grasp  of  the  human  intellect. 
Sometimes  the  principle  itself,  or  the  Ground  of  Division, 
which  determines  the  classification  of  a  whole  set  of  phe- 
nomena, is  altered ;  as  we  find  a  greater  number  of  the 
attributes  of  these  phenomena  to  be  in  constant  companion- 
ship with  some  one  or  more  traits  hitherto  disregarded  as 
of  little  account,  a  differently  constituted  hierarchy  of  Con- 
cepts, founded  upon  these  traits,  is  adopted.  This  may  be 
called  an  improvement  in  the  Method,  rather  than  an 
actual  enlargement  of  the  domain,  of  Science.  Thus  the 
Natural  System  was  substituted  for  the  Linnaean  classifica- 
tion of  plants,  and  an  improvement  almost  equally  exten- 
sive was  made  by  Cuvier  in  the  arrangement  of  the  ani- 
mal kingdom.  But  most  of  the  questions  and  problems 
which  Science  encounters  in  its  progress  relate  to  suc- 
cessive improvements  and  extensions  of  the  classification 
which,  in  all  its  main  features,  was  long  since  formed,  and 
not  to  the  substitution  of  an  entirely  different  one  in  its 
place.  The  fixedness  of  language,  which  stereotypes,  as  it 
were,  the  names  and  phraseology  appropriated  to  the  old 
division,  is  a  great  obstacle  to  the  introduction  of  a  new 
one,  which  would  require  a  new  set  of  words.  The  prin- 
cipal object  of  the  researches  of  Science  is  to  determine 
whether  this  or  that  object,  or  class  of  objects,  has  the 
special  characteristics  which  entitle  it  to  be  placed  in  a 


344  APPLIED   LOGIC. 

certain  class,  and  therefore  to  be  called  by  the  name  of 
that  class.  For  instance :  —  Is  the  lightning  to  be  placed 
in  the  class  of  electrical  phenomena?  Can  the  revolution 
of  the  planets  be  reduced  to  the  phenomena  of  falling 
bodies  ?  Is  light  the  undulatory  movement  of  an  ether  ? 
Are  the  processes  of  digestion  and  assimilation  reducible 
to  the  ordinary  action  of  chemical  affinities  ?  Ought  the 
relation  of  a  motive  to  a  volition  to  be  classed  with  the 
relations  of  cause  and  effect,  or  with  those  of  mere  ante- 
cedence and  consequence  ? 

Such  questions  relate,  for  the  most  part,  not  to  some  one 
object  or  event,  but  to  whole  classes  of  phenomena,  and 
therefore  presuppose  a  classification  already  formed.  Some- 
times, indeed,  one  particular  phenomenon  of  an  anomalous 
character  may  now  be  observed  for  the  first  time;  and 
then  the  purpose  of  the  inquiry  is,  to  refer  it  to  its  proper 
class,  and  call  it  by  its  right  name.  But  such  inquiries  be- 
long usually  to  the  education  of  a  child,  who  has  not  yet 
acquired  the  amount  of  knowledge  long  since  possessed  by 
his  elders,  and  embodied  by  them  in  language  through  the 
appropriation  of  names  to  the  different  Concepts.  But 
Science  advances  almost  exclusively  by  the  resolution  of 
problems  which  concern  whole  classes  of  objects,  and  a 
single  phenomenon  is  observed  and  experimented  upon 
only  as  a  typical  specimen  of  its  class,  and  therefore,  as 
leading  to  conclusions  which  affect  all  that  are  called  by 
the  same  name.  Thus,  Franklin  experimented  with  his 
kite  upon  a  particular  thunder-cloud,  but  only  because  this 
one  represented  to  his  mind  the  whole  class  of  meteoro- 
logical phenomena  whose  characteristics  he  was  investi- 
gating. This,  indeed,  is  the  difference  between  the  intel- 
lect of  a  common  man  and  that  of  a  philosopher.  The 
latter  flies  at  once  to  generalities  ;  the  former  wonders  at 
the  individual  case,  and  seldom  goes  beyond  it. 

"  From  the  moment  an  isolated  fact  is  discovered,"  says 


APPLIED  LOGIC.  345 

Hamilton,  "  we  endeavor  to  refer  it  to  other  facts  which  it 
resembles.  Until  this  be  accomplished,  we  do  not  view  it 
as  understood.  This  is  the  case,  for  example,  with  sulphur, 
which,  in  a  certain  degree  of  temperature,  melts  like  other 
bodies ;  but  at  a  higher  degree  of  heat,  instead  of  evapo- 
rating, again  consolidates."  Another  example  may  be 
taken  from  the  General  Fact,  which  some  will  call  a  Law 
of  Nature,  that  all  bodies  give  out  heat  on  passing  from  a 
gaseous  to  a  liquid,  or  from  a  liquid  to  a  solid,  state ;  in 
other  words,  that  contraction  of  bulk  is  attended  or  occa- 
sioned by  loss  of  heat,  and  expansion  of  bulk  by  addition 
or  absorption  of  heat.  Yet  clay  is  known  to  contract  from 
the  application  of  heat ;  and  though  water  contracts  in  bulk 
when  it  is  cooling  down  to  as  low  a  temperature  as  40°,  yet 
as  it  falls  below  that  point  it  expands  again,  and  in  the 
act  of  congelation  there  is  a  sudden  and  considerable  in- 
crease of  bulk.  Our  natural  love  of  unity,  or  disposition 
to  reduce  corresponding  phenomena  to  one  class  or  Law, 
does  not  allow  us  to  rest  in  the  consideration  that  such 
cases  are  anomalous,  or  isolated  exceptions.  We  seek 
either  for  a  new  expression  of  the  Law,  which  shall  cover 
also  these  apparent  exceptions,  or  for  the  discovery  of 
some  attribute  of  these  now  isolated  cases  which  shall 
harmonize  them  with  the  Law  as  already  expressed.  When 
the  facts  are  thus  generalized,  or  brought  together  under 
one  Concept  and  name,  "  our  discontent  is  quieted,"  Ham- 
ilton continues,  "  and  we  consider  the  generality  itself  as 
tantamount  to  an  explanation.  Why  does  this  apple  fall 
to  the  ground  ?  Because  all  bodies  gravitate  towards  each 
other.  Arrived  at  this  General  Fact,  we  inquire  no  more, 
although  ignorant  now,  as  previously,  of  the  cause  of  gravi- 
tation ;  for  gravitation  is  nothing  more  than  a  namem  for  a 
General  Fact,  the  why  of  which  we  know  not.  A  mystery, 
if  recognized  ar>  universal,  would  no  longer  appear  myste- 
rious." 

15* 


346  APPLIED  LOGIC. 

We  now  see  how  it  is  that  the  successive  discoveries, 
and  consequent  enlarged  and  improved  generalizations,  of 
Science  are  embodied,  as  fast  as  they  are  made,  in  lan- 
guage, so  that  we  learn  them  through  the  simple  mode  of 
gradually  acquiring  the  use  of  our  mother  tongue.  This  is 
done  to  some  extent  by  the  actual  introduction  of  new 
words  and  names,  these  being  necessary  to  designate  the 
new  groups  and  Concepts  which  the  improved  classification 
requires.  But  it  is  effected  still  more  largely  by  modifying 
and  enlarging  the  connotation  of  words  already  in  use. 
For  a  time,  these  new  elements  of  phraseology  are  in  cur- 
rent use  only  among  a  small  circle  of  scientific  inquirers, 
whose  labors  have  made  them  necessary.  But  gradually 
they  creep  out  into  the  ordinary  dialect  of  the  market,  the 
parlor,  and  the  newspaper,  and  are  naturalized  there,  and 
taught  to  children  as  fast  as  children  learn  to  speak.  How 
much  more  knowledge  is  now  necessarily  acquired  in  learn- 
ing the  use  of  the  English  language,  than  was  gained  from 
such  learning  only  one  or  two  centuries  ago  I 

The  same  considerations  of  interest  and  convenience,  of 
immediate  relation  to  the  curiosity  or  the  physical  wants 
of  men,  which  determine  us  to  classify  and  name  some 
of  our  individual  observations  and  experiences,  to  the  ex- 
clusion of  many  others,  also  guide  us  in  the  selection  of 
those  groups  of  Concepts  which  we  enlarge,  develop,  and 
methodize  into  distinct  Sciences.  As  many  objects  and 
events  do  not  need  to  be  classified  because  they  are  not 
worth  remembrance,  so  the  classification  of  many  others 
needs  not  to  be  extended  beyond  the  first  and  most  ele- 
mentary stage,  because  a  Science  elaborated  out  of  them 
would  neither  interest  us  nor  minister  to  our  necessities. 
We  .do  not  chronicle  petty  occurrences,  we  do  not  study 
out  and  subsequently  generalize  the  insignificant  relations 
of  unimportant  objects  to  each  other.  But  as  circum- 
stances change  and  knowledge  is  enlarged,  what  formerly 


APPLIED  LOGIC.  347 

seemed  trivial  often  assumes  a  new  dignity  and  interest, 
or  is  unexpectedly  found  to  be  subservient  to  some  great 
purpose.  A  new  Science,  or  department  of  Science,  is  thus 
formed,  perhaps  to  be  carried  up  by  subsequent  discoveries 
and  generalizations  higher  than  any  of  those  formerly  cul- 
tivated. How  many  new  departments  of  study  and  re- 
search have  thus  been  opened  within  the  last  few  genera- 
tions !  The  Sciences  of  Geology,  Ethnology,  Comparative 
Philology,  and  Political  Economy  are  hardly  more  than  a 
century  old.  The  moderns  know  more  than  the  ancients, 
not  so  much  because  they  know  the  same  things  more  per- 
fectly, as  because  their  investigations  are  extended  over  a 
larger  range  of  objects. 

Hence  it  is  easy  to  see  why  the  numerous  attempts  that 
have  been  made  to  classify  the  Sciences,  and  thereby  to 
reduce  them  into  one  complete  and  orderly  system  of 
human  knowledge,  have  not  been  more  successful.  The 
Sciences  have  not  been  formed  on  any  predetermined  and 
systematic  plan,  with  a  view  of  covering  the  whole  ground 
of  inquiry  ;  but  they  have  grown  by  a  natural  and  irregular 
development,  corresponding  both  to  the  ever  increasing 
wants  and  stimulated  curiosity  of  those  who  prosecute 
them,  to  the  different  aptitudes  of  the  various  classes  of 
objects  to  be  digested  into  system  and  divided  by  obvious 
lines  of  demarcation,  and  especially  to  the  facility  with 
which  our  conclusions  respecting  these  objects  may  be 
drawn  without  the  aid  of  observation  and  experience. 
Such  a  survey  of  all  that  is  possible  to  be  known,  com- 
pared with  all  that  is  actually  known,  as  Bacon  attempted 
to  make  in  his  treatise  on  the  "  Advancement  of  the  Sci- 
ences," must  always  disclose,  as  it  did  to  him,  many  lacunce, 
or  gaps  which  it  is  necessary  to  fill,  before  man  can  be  said 
even  to  have  entered  upon  all  the  avenues  which  lead  to 
truth.  Divisions  of  the  Sciences,  like  those  which  have 
been  devised  by  Bacon,  Locke,  Ampere,  Comte,  Wilson, 


348  APPLIED  LOGIC. 

and  others,  lnust  always  be  imperfect,  or,  if  they  approxi* 
mate  completeness,  must  always  indicate  at  least  as  many 
blanks  as  there  are  departments  already  occupied.  Whether 
we  try  to  distribute  the  various  branches  of  knowledge,  as 
Bacon  did,  according  to  the  different  faculties  of  the  mind 
which  they  respectively  call  into  play;  or,  with  Locke, 
according  to  the  several  ends  in  view ;  or,  with  Descartes, 
as  followed  by  Comte,  according  to  the  order  of  their  de- 
velopment, as  determined  by  their  degrees  of  simplicity ;  — 
some  Sciences  will  appear  redundant,  others  as  defective, 
and  many  as  having  an  equally  good  title  to  be  ranked 
under  two  or  three  different  heads. 

As  one  of  the  best  specimens  of  these  attempts  at 
classification,  we  may  take  Dr.  Thomson's  account  of  the 
arrangement  proposed  by  Comte,  on  the  basis  of  Descartes's 
aphorism,  that  knowledge  should  advance  from  the  simpler 
to  the  more  complex  phenomena. 

"  Mathematics,  or  the  science  of  quantities,  is  at  once  the 
most  simple  in  its  elements  and  the  most  general  in  its  ap- 
plication, entering,  more  or  less,  into  all  the  sciences  of  Na- 
ture, and  constituting  almost  the  whole  of  that  which  comes 
next  it  in  the  order  of  dependence.  Astronomy,  or  the 
science  of  the  heavenly  bodies,  is  the  application  of  mathe 
matical  truths  to  the  laws  of  matter  and  motion ;  matter 
and  the  motions  of  material  bodies  being  the  new  concep- 
tions which  belong  to  this  science.  Physics,  being  the 
science,  or  rather  group  of  sciences,  which  is  conversant 
with  the  general  laws  of  the  world,  so  far  as  they  relate  to 
beings  without  life  or  organization,  would  come  next ;  and 
it  imports,  in  addition  to  the  conceptions  of  Astronomy, 
those  of  light,  of  heat,  of  sound,  of  electricity,  of  magnetism, 
and  many  others.  Chemistry  would  rank  next,  which  is 
the  science  of  the  decomposition  and  combinations  of  the 
various  substances  that  compose  and  surround  the  earth. 
Next  in  order  of  complexity  would  rank  Physiology,  founded 


APPLIED  LOGIC.  349 

on  the  additional  conception  of  vegetable  and  animal  life. 
To  this  would  succeed  Anthropology,  or  the  science  of 
man's  nature ;  and  to  this,  Social  Science,  which  ascertains 
the  laws  that  govern  men  when  combined  in  cities  and  na- 
tions. Each  of  these  departments  may  be  divided  into 
many  branches ;  as  Physics  into  Acoustics,  Optics,  Elec- 
tricity, and  the  like ;  or  Social  Science  into  Morals,  Poli- 
tics, Political  Economy,  Law,  and  the  like. 

"  On  comparing  scientific  works,  differences  in  the  mode 
of  teaching  the  same  subject  become  apparent.  In  one, 
the  pure  theory  of  Astronomy  is  presented ;  in  another,  the 
striking  features  of  its  historical  progress  as  a  science,  with 
speculations  on  the  historical  sequence  of  the  phenomena 
themselves ;  in  a  third,  the  practical  applications  of  which 
the  Science  admits  in  respect  to  the  comfort  and  progress  of 
mankind.  This  threefold  mode  of  treatment  runs  through 
all  the  Sciences,  and  in  a  table  of  them  might  well  be  ex- 
pressed. The  classification  would  thus  embody  all  that  is 
valuable  of  another  system  of  classes,  that  according  to  the 
purpose  towards  which  the  Science  was  directed. 

"A  classification  which  advances  on  Descartes's  principle, 
from  the  more  simple  to  the  more  complex  subjects,  which 
commences  from  the  notions  of  extension  and  quantity, 
and  proceeds  through  material  things  up  to  living,  intelli- 
gent, and  moral  agents,  ought  to  coincide  with  the  order 
in  which  the  sciences  themselves  have  reached  maturity. 
And  this  it  certainly  does.  Mathematics  had  made  good 
its  ground  when  Astronomy  was  yet  in  its  infancy ;  Physics 
began  to  obtain  a  sure  footing  later  than  either ;  whilst  the 
Sciences  which  relate  to  Life  are  still  very  immature  ;  and 
some  of  the  main  problems  of  Social  Science  are  yet  mat- 
ter of  controversy  even  in  our  own  days." 

It  is  an  obvious  imperfection  of  this  scheme,  that  it  takes 
no  notice  of  the  numerous  branches  of  that  Science,  Natu- 
ral History,  which,  as  it  depends  solely  upon  observation, 


350  APPLIED  LOGIC. 

and  thus  gives  us  our  first  knowledge  of  all  the  objects  of 
study,  would  seem  to  constitute  the  basis  of  all  the  other 
Sciences.  In  explanation  of  this  defect,  Comte  remarks, 
"  we  must  distinguish  between  the  two  classes  of  Natural 
Science ;  —  the  abstract  or  general,  which  have  for  their 
object  the  discovery  of  the  Laws  which  regulate  phenomena 
in  all  conceivable  cases;  and  the  concrete,  particular,  or 
descriptive,  which  are  sometimes  called  Natural  Sciences 
in  a  restricted  sense,  whose  function  it  is  to  apply  these 
Laws  to  the  actual  history  of  existing  beings.  The  first 
are  fundamental ;  and  our  business  is  with  them  alone,  as 
the  second  are  derived,  and,  however  important,  not  rising 
into  the  rank  of  our  subjects  of  contemplation.  We  shall 
treat  of  Physiology,  but  not  of  Botany  and  Zoology,  which 
are  derived  from  it.  We  shall  treat  of  Chemistry,  but  not 
of  Mineralogy,  which  is  secondary  to  it."  But  this  remark 
is  inconsistent  with  the  previous  assertion,  that  this  order 
of  classification  "  coincides  with  the  order  in  which  the 
Sciences  themselves  have  reached  maturity.' '  In  the  order 
of  time,  certainly,  Zoology  and  Botany  had  been  cultivated 
to  a  considerable  extent  before  men  had  obtained  more 
than  the  crudest  notions  of  the  physiological  processes  of 
animal  and  vegetable  life  ;  just  as  Civil  History,  the  ba:is 
of  another  department,  had  been  very  fully  treated  before  it 
first  suggested  the  idea  of  Social  Science.  In  what  may 
be  called  the  logical  order,  or  the  order  of  ideas,  however, 
it  is  true  that  the  Sciences  which  embody  principles  and 
general  results  take  precedence  of  those  which  afford  only 
the  material  of  knowledge. 


DEMONSTRATIVE  REASONING.  351 


CHAPTER   XI. 

DEMONSTRAHVE  REASONING  AND  DEDUCTIVE  EVIDENCE. 

WE  have  already  said,  that  the  principal  object  of  the 
researches  of  Science  is,  to  determine  whether  this 
or  that  object,  or  class  of  objects,  has  the  special  character- 
istics which  entitle  it  to  be  placed  in  a  certain  class,  and 
called  by  a  certain  name. 

Most  of  such  questions,  if  they  relate  only  to  one  thing, 
or  to  a  very  few  things,  are  answered  directly,  and  with- 
out difficulty,  by  observation  or  intuition.  We  answer  one 
of  them,  in  fact,  whenever  we  perceive  any  object  and  call 
it  by  its  appropriate  Common  Name.  For  instance  ;  —  this 
thing  which  I  now  hold  in  my  hand  I  call  a  pen,  a  rose,  or 
an  apple,  because  I  perceive  that  it  has  the  attributes  which 
are  the  Marks  connoted  by  that  name.  In  like  manner,  I 
pronounce  the  animals  now  before  me  to  be  dogs,  horses,  or 
cows,  according  as  I  recognize  their  distinctive  qualities. 

Writers  like  Dr.  Brown,  Mr.  J.  S.  Mill,  and  Mr.  Bailey, 
who  have  laboriously  attempted  to  restrict  the  range  and 
depreciate  the  utility  of  the  Syllogistic  process,  have  seem- 
ingly failed  to  notice  the  fact,  that  we  must  reason  syllogis- 
tically  whenever  we  use  language  with  any  perception  of 
its  meaning,  —  that  is,  when  we  call  anything  by  its  appro- 
priate name.  If  I  had  not  already  spread  out  before  my 
mind  the  Marks  which  constitute  the  Intension  of  the 
Concept  apple,  or  rose,  I  could  not  designate  the  object 
now  presented  to  me  by  that  appellation.  This  process  of 
reasoning,  which  we  are  performing  almost  every  moment 


l>0'1  DEMONSTRATIVE   REASONING 

of  our  lives,  and  therefore  so  quickly  and  easily  that  its 
several  steps  are  taken  almost  unconsciously,  is  thus  spread 
out  into  the  formal  process. 

The  Concept  or  Class-notion  apple  has,  as  Marks,  a 
nearly  spherical  shape,  a  red  color,  a  moderate  hardness, 
and  a  certain  smell ; 

This  object  has  all  these  Marks  ; 

Therefore,  this  object  is  an  apple. 

This  is  what  Hamilton  calls  Reasoning  in  Intension,  for, 
in  each  of  the  Premises,  the  Predicate  is  contained  in  the 
Subject.  Moreover,  the  Reasoning  is  not  only  logical,  — 
L  e.  valid  in  Form,  but  it  is  also  Demonstrative, — i.  e.  abso- 
lutely certain  in  respect  to  its  Matter.  It  is  Demonstrative, 
because  the  Major  Term,  which  is  here  the  Subject  of  the 
Major  Premise,  is  a  Concept  or  Class-notion,  which,  being 
a  mere  creation  of  the  mind,  cannot  have  any  other  Marks 
or  qualities  than  those  which  we  voluntarily  attribute  to  it. 
As  we  know  by  Intuition,  that  the  object  has  all  the  Marks 
which  we  included  in  the  Concept,  it  is  certain  that  it 
should  be  designated  by  the  name  of  that  Concept,  —  that 
is,  that  it  should  be  included  under  its  Extension. 

On  the  other  hand,  if  the  Reasoning  is  made  to  concern, 
not  a  mere  Concept  in  the  mind,  but  a  class  of  real  things, 
which,  as  we  have  seen,  always  have  an  unknown  and  un- 
knowable number  of  qualities  and  relations,  then  I  cannot 
be  sure  that  the  object  in  question  possesses  all  these  quali- 
ties, but  can  only  doubtfully  infer  that  it  has  all,  because  I 
know  that  it  possesses  some,  of  the  more  important  of  them. 
An  element  of  uncertainty  is  introduced ;  the  Reasoning 
ceases  to  be  Demonstrative,  and  becomes  merely  Probable 
or  contingent.  For  instance;  —  if,  in  the  Major  Premise 
of  the  preceding  Syllogism,  we  say,  not  "  the  Concept  or 
Class -notion  apple,"  but  "All  apples"  —  i.  e.  All  the 
actual  objects  which  we  have  been  accustomed  to  call  ap- 
ples —  "  have  a  nearly  spherical  shape,  a  red  color,  a  mod- 


AND   DEDUCTIVE  EVIDENCE.  353 

erate  hardness,  and  a  certain  smell "  ;  then,  though  f*  this 
object  has  all  these  Marks,"  I  cannot  be  sure  that  "it  is  an 
apple."  It  may  be  only  a  wax  counterfeit,  and  the  decep- 
tion wou^i  instantly  be  detected  by  the  taste,  which  quality 
was  not  included  in  the  enumeration.  The  Reasoning  v 
still  valid  in  Form,  but  the  Major  Premise  is  false ;  it  cov- 
ers up  the  Fallacy  fictce  universalitatis.  In  order  to  be 
sure  that  an  object  is  properly  ranked  under  a  given  class, 
we  must  be  certain  that  it  contains  all  the  original  and 
essential  qualities  of  the  objects  denoted  by  the  class-name ; 
and  this  certainty,  in  the  case  of  real  things,  is  unattain- 
able. In  our  conception,  we  may  arbitrarily  restrict  the 
meaning  of  the  word  apple,  so  as  to  exclude  the  quality  of 
taste;  and  in  this  sense,  the  wax  counterfeit  is  properly 
called  an  apple.  But  in  speaking  to  others,  the  word 
would  be  understood  to  signify  all  the  qualities  possessed 
by  the  real  things,  viz.  this  sort  of  fruit ;  and  in  this  mean- 
ing, the  wax  substitute  is  not  an  apple. 

We  can  now  see  why  the  Reasonings  of  the  mathema- 
tician are  Demonstrative,  while  those  of  the  zoologist,  the 
botanist,  and  other  naturalists  who  deal  only  with  real 
things,  are  merely  Probable  or  contingent.  The  Form  is 
always  the  same  ;  Reasoning,  as  such,  must  always  be 
Syllogistic ;  and  when  the  rules  of  Pure  Logic  are  duly 
observed,  the  Consequence,  or  the  mere  deduction  of  the 
Conclusion  from  the  Premises,  must  be  absolutely  cer- 
tain. The  difference,  then,  concerns  the  Premises  only, 
the  truth  of  which,  as  we  have  seen,  is  not  guaranteed  by 
the  principles  of  Logic.  The  universal  rule,  that  the  Mid- 
dle Term  must  always  be  distributed,  requires  that  the 
pre  designation  all,  or  none,  should  appear  in  at  least  one 
of  the  Premises.  Now,  our  knowledge  of  real  things  is 
derived  solely  from  experience ;  and  experience,  as  has 
been  mentioned,  must  be  restricted,  from  its  very  nature, 
to  a  limited  n  imber  of  examples.     In  respect  to  real  ol>- 


854  DEMONSTRATIVE  REASONING 

jects  and  events,  it  can  never  extend  either  to  the  inclu 
sion  or  the  exclusion  of  all;  it  can  never  pronounce  with 
certainty  either  upon  all,  or  none.  Only  with  reference  to 
a  certain  class  arbitrarily  formed  by  the  Understanding,  — 
to  the  very  things  which  I  am  now  thinking  of,  or  which 
I  have  actually  observed,  and  to  none  others,  — to  the 
things  which  are  included  under  this  Definition,  and  to 
these  only,  —  can  the  finite  understanding  of  man,  so  far 
as  it  is  enlightened  only  by  experience,  safely  pronounce 
upon  all  or  none.  Without  such  limitations,  naturalists, 
and  all  others  who  seek  to  educe  Science  from  mere  expe- 
rience, can  never  speak  of  all  or  none,  without  falling  into 
the  Fallacy  fictce  universalitatis. 

The  mathematician  deals  only  with  certain  Concepts  of 
Quantity,  whether  continuous  or  discrete,  which  are  pre- 
cisely limited  and  determined  by  the  Definitions  that  he 
employs.  The  propositions  which  he  establishes  do  not 
concern  circular  objects  and  triangular  objects,  which  are 
real  things,  but  circles  and  triangles,  which  are  imaginary 
things  as  conceived  by  the  Understanding,  and  which  are 
restricted  by  their  Definitions  to  the  possession  of  those 
qualities  only  which  Thought  voluntarily  attributes  to 
them.  Hence,  the  conclusions  which  the  mathematician 
forms  respecting  them  are  not  liable  to  be  vitiated  by  the 
intrusion  of  any  unexpected  and  counteracting  elements. 
Any  theorem,  therefore,  which  is  proved  of  one,  must  hold 
good  of  all;  any  property  which  cannot  belong  to  one,  can 
be  possessed  by  none,  of  the  class  thus  defined.  The  sune 
measure  of  certainty  which  the  student  of  nature  obtains 
by  Intuition  respecting  a  single  real  object,  the  mathe- 
matician acquires  respecting  a  whole  class  of  imaginary 
objects,  because  the  latter  has  the  assurance,  which  the  for- 
mer can  never  attain,  that  the  single  object,  which  he  is 
contemplating  in  Thought,  is  a  perfect  representative  of  its 
whole  class ;  he  has  this  assurance,  because  the  whole  class 


AND   DEDUCTIVE   EVIDENCE.  355 

exists  only  in  Thought,  and  are  therefore  all  actually  before 
him,  or  present  to  consciousness.  For  example ;  this  bit 
of  iron,  I  find  by  direct  observation,  melts  at  a  certain 
temperature ;  but  it  may  well  happen  that  another  piece 
of  iron,  quite  similar  to  it  in  external  appearance,  may  be 
fusible  only  at  a  much  higher  temperature,  owing  to  the 
unsuspected  presence  with  it  of  a  little  more,  or  a  little  less, 
carbon  in  composition.  But  if  the  angles  at  the  basis  of 
this  triangle  are  equal  to  each  other,  I  know  that  a  corre- 
sponding equality  must  exist  in  the  case  of  every  other 
figure  which  conforms  to  the  Definition  of  an  isosceles 
triangle  ;  for  that  Definition  excludes  every  disturbing  ele- 
ment. The  conclusion  in  this  latter  case,  then,  is  Univer- 
sal, while  in  the  former,  it  can  be  only  Singular  or  Par- 
ticular. 

Conclusions  which  are  demonstratively  certain  and  abso- 
lutely universal  can  be  obtained  only  when  we  are  reason- 
ing about  abstract  conceptions.  In  the  case  of  natural 
objects  and  events,  which  can  be  known  only  through  ex- 
perience, we  approximate  universality  and  certainty  in  rea- 
soning only  by  the  aid  of  Induction  and  Analogy.  The 
lack  of  certainty  is  a  consequence  of  the  lack  of  univer- 
sality. No  doubt  affects  the  few  instances  which  I  am 
now  actually  observing,  or  which  are  present  to  sense  or 
consciousness.  Of  these,  I  am  as  certain  as  of  any  conclu- 
sions in  arithmetic  or  geometry.  The  doubt  comes  in  only 
when  I  attempt  to  extend  the  conclusion  from  some,  which 
I  have  examined,  to  all  others,  of  which  I  know  nothing, 
except  from  testimony,  Induction,  or  Analogy.  And  this 
doubt  is  inevitable  ;  no  matter  how  many  cases  have  been 
examined,  experience  can  never  extend  to  all.  The  fact 
that  all  matter  gravitates,  or  has  weight,  is  a  truth  which 
rests  upon  as  large  a  testimony  from  experience  as  has  ever 
been  collected.  Yet  the  chemist  will  readily  admit  that  it 
is  not  only  conceivable,  but  we  may  almost  say  probable, 


-356  DEMONS'!  RATI VE   REASONING 

that  some  of  the  imponderable  agents,  as  they  are  called,  — 
heat,  light,  electricity,  &c, —  may  at  last  be  found  to  be 
material ;  and  the  astronomer  has  not  yet  proved  entirely 
to  his  satisfaction,  that  the  law  of  gravitation  is  universal 
throughout  the  stellar  system.  From  the  nature  of  the  case, 
he  would  say,  the  fact  does  not  admit  of  absolute  proof. 

It  appears,  then,  that  the  range  of  Deductive  reasoning 
and  Demonstrative  proof  is  not  confined  to  pure  Mathe- 
matics. Whenever  the  objects  about  which  we  reason  are 
pure  Concepts,  or  mere  creations  of  the  intellect,  strictly 
limited  by  Definition,  and  thus  guarded  against  reference 
to  things  actually  existent  in  Nature,  our  conclusions  re- 
specting them,  if  obtained  in  strict  uniformity  with  logical 
rules,  are  as  absolute  as  the  truths  of  the  multiplication- 
table.  But  Mathematics,  it  must  be  admitted,  afford  vastly 
the  larger  number  of  conclusions  of  this  class  ;  in  no  other 
science  is  Demonstrative  reasoning  either  carried  so  far,  or 
so  fruitful  in  results.  This  peculiarity  seems  to  be  due 
to  the  nature  of  those  Concepts,  quantity,  space,  and  num- 
ber, with  which  the  mathematician  deals.  Two  of  these, 
quantity  and  number,  are  universal  attributes,  as  they  belong 
to  all  things,  both  to  objects  of  sense  and  consciousness  ;  and 
the  third,  space  or  extension,  is  an  attribute  of  all  external 
things.  They  are  suggested  to  us  on  a  greater  variety  of 
occasions  than  any  other  qualities,  and  thus  are  more  fre- 
quent objects  of  contemplation,  and  more  fully  determined. 
u  Propositions  concerning  numbers,"  as  Mr.  Mill  observes, 
"  have  this  remarkable  peculiarity,  that  they  are  proposi- 
tions concerning  all  things  whatever,  —  all  objects,  all  ex- 
istences of  every  kind,  known  to  our  experience.  All 
things  possess  quantity;  consist  of  parts  which  can  be  num- 
bered ;  and,  in  that  character,  possess  all  the  properties 
which  are  called  properties  of  numbers." 

Again,  the  various  modes,  properties,  and  relations  of 
quantity,  space,  and  number  admit  of  being  more  accurately 


AND   DEDUCTIVE   EVIDENCE.  857 

defined  and  clearly  determined  than  those  of  any  other 
class  of  ideas ;  they  are  separable  from  each  other  by  lines 
of  demarcation  that  cannot  be  overlooked  or  mistaken. 
Differences  of  degree,  with  which  we  are  chiefly  concerned 
in  the  case  of  all  other  qualities,  are  not  by  any  means  so 
definite,  as  they  are  shaded  into  each  other  by  impercep- 
tible gradations  ;  their  minute  differences  are  inappreciable 
either  by  the  senses  or  by  the  understanding.  But  the 
difference  between  two  quantities,  whether  of  number  or 
extension,  may  be  reduced  as  low  as  we  please,  and  still 
remain  as  distinct  to  our  apprehension  as  if  it  were  world- 
wide. 

But  the  chief  peculiarity  of  these  three  Concepts,  which 
causes  them  to  afford  so  broad  and  fruitful  a  field  for  De- 
monstrative reasoning,  is  the  measureless  variety  of  accu- 
rately determinable  relations  in  which  all  their  modes  stand 
to  each  other.  Any  one  quantity  stands  in  a  perfectly  con- 
ceivable ratio  —  whether  it  can  be  exactly  expressed  in 
numbers  or  not  —  to  every  other  quantity,  and  also  has  a 
countless  number  of  peculiar  relations  in  which  it  stands  to 
many  at  once.  Attempt  to  enumerate,  for  instance,  the 
properties  of  the  number  9 ;  —  that  it  is  the  square  of  3, 
the  square-root  of  81,  the  double  of  4J,  the  half  of  18, 
&c,  —  and  we  soon  abandon  the  undertaking  in  despair. 
And  when  we  come  to  think  of  the  relations  of  these  rela- 
tions, as  in  the  doctrine  of  proportions,  it  becomes  evident 
that  the  properties  of  quantity  are  too  great  to  be  num- 
bered.    The  field  of  investigation  is  infinite. 

These  innumerable  and  perfectly  definite  relatior  y  which 
subsist  between  distinct  quantities,  furnish  an  inexhaustible 
number  of  Middle  Terms,  through  which  we  obtain,  by 
Mediate  Inference,  such  Conclusions  as  are  not  apparent  at 
a  glance,  or  by  direct  Intuition.  When  the  geometer,  for 
instance,  cannot  determine  directly  the  distance  from  one 
point  to  another,  he  constructs  a  triangle,  the  base  of  which, 


358  DEMONSTRATIVE  REASONING 

with  its  adjacent  angles,  as  accessible,  can  be  easily  meas- 
ured ;  and  he  can  then  deduce  the  required  distance,  or 
the  height  of  the  triangle,  from  the  known  relations  which 
exist  between  it  and  the  quantities  which  he  has  thus  di- 
rectly determined.  In  like  manner,  the  value  of  one  or 
more  unknown  quantities,  symbolically  represented  in  an 
algebraic  equation,  is  deduced  from  some  of  the  given  rela- 
tions which  subsist  between  them  and  the  known  quan- 
tities, with  which  they  are  taken  in  connection.  Indeed, 
the  peculiar  function  of  algebraic  science  is  to  determine 
general  relations  between  different  groups  and  classes  of 
magnitudes,  these  general  ratios,  proportions,  and  analyses 
being  subsequently  applied  by  the  geometer  and  the  arith- 
metician to  the  solution  of  particular  problems.  The  mere 
construction  of  a  geometrical  diagram  enables  us  to  see  the 
use  which  is  made  of  one  or  two  known  relations  between 
several  quantities,  as  means  of  determining  indirectly  oilier 
relations  between  them  which  cannot  be  directly  meas- 
ured. The  diagram  is  only  a  means  of  making  clear  to 
onr  apprehension  the  fact,  that  the  same  straight  line,  or 
length  already  determined,  is  at  once  the  base  of  a  triangle, 
the  radius  of  a  circle,  the  side  of  a  square,  &c. ;  then  this 
line  may  be  used  as  a  Middle  Term,  or-means  of  proving 
syllogistically  what  the  other  properties  and  dimensions, 
hitherto  unascertained,  of  this  triangle,  circle,  and  square 
must  be.  Thus  to  ascertain  a  new  property  of  a  former 
object  of  Thought  is  to  advance  a  step  in  the  classifications 
which  the  mind  is~  continually  forming,  enabling  us  to  refer 
this  object,  perhaps  hitherto  anomalous,  to  its  proper  class. 
The  diagram,  indeed,  is  a  Singular  instance  ;  but  what  it 
enables  us  to  discover  is  a  General  Truth  ;  for,  as  already 
remarked,  we  know  that  this  one  instance  is  a  perfect  rep- 
resentative of  its  whole  class,  since  that  class  exists  only  in 
our  Thought,  and  is  therefore  perfectly  known.  The  little 
triangle  which  I  am  contemplating  as  drawn  on  paper  cor- 


AND  DEDUCTIVE  EVIDENCE.  859 

responds  perfectly,  in  all  particulars  that  can  be  essential  for 
the  Reasoning,  to  the  magnificent  one,  having  as  its  base 
line  the  diameter  of  the  earth's  orbit,  which  the  astrono- 
mer, when  he  would  determine  the  distance  of  a  fixed  star, 
imagines  to  be  erected  in  the  heavens. 

These  considerations  appear  to  me  to  evince  very  clearly, 
that  the  peculiar  cogency  and  fruitfulness  of  mathematical 
reasoning  do  not  arise,  as  Kant  maintains,  from  the  fact 
that  it  concerns  nothing  but  Space  and  Time,  ^nd  that 
Space  and  Time  exist  only  in  our  minds.  The  soEr  object 
of  this  sort  of  reasoning  seems  to  be  quantity  in  its  various 
forms  ;  and  reasoning  would  be  equally  Demonstrative,  if 
it  related  to  any  other  single  attribute  of  things  considered 
abstractly,  or  as  we  conceive  it  apart  from  all  other  proper- 
ties with  which  it  is  united  in  the  actual  constitution  of 
things.  The  fact  that  Quantity  is  a  universal  attribute,  be- 
longing to  all  objects  of  Thought  whatever,  explains  the 
broad  scope  and  general  applicability  of  mathematical  rea- 
soning ;  while  its  peculiar  fruitfulness,  or  the  vast  number 
of  truths  which  it  brings  to  light,  appears  to  proceed  from 
the  countless  number  and  definite  character  of  the  relations 
which  subsist  between  different  quantities.  No  other  attri- 
bute presents  itself  so  universally,  or  in  modes  at  once  so 
numerous  and  so  distinct,  capable  alike  of  indefinite  aug- 
mentation and  diminution.  The  field  is  boundless,  and  we 
advance  over  any  portion  of  it  with  the  precision  and  cer- 
tainty in  every  movement  which  admit  neither  error  nor 
doubt. 

The  views  which  have  now  been  presented  enable  us  to 
refute  the  doctrine,  originally  proposed,  as  Mr.  Stewart 
thinks,  by  Leibnitz,  that  the  certainty  of  mathematical 
reasoning  depends  upon  the  fact,  that  all  the  evidence  on 
which  it  is  supported  may  be  resolved,  in  the  last  analysis, 
into  the  perception  of  identity ; — "the  innumerable  vari- 
ety of  propositions  which  have  been  discovered,  or  which 


360  DEMONSTRATIVE  REASONING 

remain  to  be  discovered  in  the  science,  being  only  diversi- 
fied expressions  of  the  simple  formula,  a  =  a."  It  is  true 
that  this  theory  correctly  presents  the  form,  not  only  of 
mathematical  reasoning,  but  of  all  reasoning  whatever  ; 
for  we  have  shown  that  every  Affirmative  Judgment,  in  a 
certain  sense,  or  with  reference  to  the  denotation  of  the 
Concepts  which  it  concerns,  is  an  equation  of  its  two 
Terms,  The  formula,  A  is  B,  to  which  all  conceivable 
Affirmative  Judgments  may  be  reduced,  is  resolvable,  in 
this  sense,  as  B  equals  A,  into  A  =  A,  But  the  peculiar 
cogency  of  mathematical  evidence  cannot  be  explained  by 
the  possession  of  an  attribute  which  does  not  distinguish  it 
from  Moral  Reasoning.  In  reference  to  the  connotation 
of  its  Terms,  a  Judgment  does  not  express  an  equation, 
but  the  inclusion  of  an  object  in  a  class,  and  the  conse- 
quent possession  by  that  object  of  the  peculiar  attributes 
of  that  class.  In  tins  sense,  the  signification  is,  not  that 
the  Subject  equals  the  Predicate,  but  that  it  possesses  one 
or  more  of  the  attributes  of  the  Predicate,  or  possesses  the 
Predicate  itself  as  one  of  its  own  attributes.  The  doctrine 
which  we  are  considering  owes  its  plausibility  to  a  con- 
fusion of  the  significance  of  these  two  very  different  words, 
identity  and  equivalence.  When  the  geometer  proves  the 
area  of  a  circle  to  be  equal  to  that  of  a  triangle  having  the 
circumference  for  its  base  and  the  radius  for  its  altitude, 
he  certainly  does  not  mean  that  it  is  identical  with  such  a 
triangle,  but  only  that  it  is  equivalent  to  it  in  a  single  re- 
spect,— viz.  in  magnitude;  they  are  not  identical,  for,  in 
shape,  they  are  wholly  unlike.  Take  even  a  simpler  case, 
which  seems  more  nearly  resolvable  into  an  expression  of 
identity :  4  =  2  -(-  2.  Even  here,  the  meaning  is  not  that 
the  two  members  of  the  equation  are  identical,  but  only 
that  the  Concept  or  group  four  is  equivalent  in  one  respect 
—  viz.  the  possession  of  an  equal  number  of  units  —  to 
the  two  groups  two  and  two.     It  is  plain  that  one  group 


AND  DEDUCTIVE  EVIDENCE.  361 

cannot  be  identical  with  two  groups,  or  that  two  distinct 
acts  of  the  mind,  each  conceiving  or  grasping  together  two 
units,  cannot  be  literally  the  same  thing  as  one  mental  act 
conceiving  four. 

The   essential   distinction   between   Pure   and   Applied 
Mathematics   consists    in    this,   that,   in   the   former,   our 
thoughts  never  go  beyond  the  conception  of  pure  quan- 
tity, or  magnitude  in  the  abstract,  considered  in  either  of 
its  two  modes,  space  or  number;  while  in  the  latter,  the 
additional   qualities   of  weight,    attraction,   impenetrability, 
elasticity,   density,  and  many  others,  are  brought  in,  not 
merely  as  they  are  conceived  in  the  mind,  but  as  they 
actually  exist,  or  are  manifested,   in  real  things.     These 
qualities  also,  so  far  as  they  are  viewed  in  the  former  light, 
that  is,   abstractly,  as  mere  Concepts  strictly  limited  by 
Definition,  may  be  reasoned  about  demonstratively  ;  though 
it  is  only  in  respect  to  their  quantity  that  the  reasoning  will 
have  any  wide  range,  or  be  fruitful  in  conclusions,  since 
they  have  not  the  numerous  and  distinctly  conceived  rela- 
tions which  subsist  between  the  innumerable  degrees  of 
Quantity.     But  if  viewed  as  actual  qualities  of  real  things, 
our  knowledge  of  them  is  derived  merely  from  experience, 
and  must  therefore  be  subject  to  all  the  limitations  and  im- 
perfections of  knowledge  so  derived.     No  Judgments  con- 
cerning them  can  be  absolute  or  universal ;  they  are  objects 
only  of  Probable  Reasoning.     Previous  to  experience,  we 
could  not  attribute  weight  to  any  material  substance,  much 
less  to  all  such  substances;  that  every  particle  of  matter 
should  attract,  would  seem  no  more  probable  than  that  it 
should  repel,  every  other  particle.     This  is  the  source  of 
Dr.  Whewell's  error  ;  because  weight,  attraction,  impene- 
trability, &c.   can  be  conceived  abstractly,   and  therefore 
be  strictly  limited  by  Definitions,  and  so  reasoned  about 
demonstratively,  he  maintains  that  the  Physical  Laws  of 
Mution  are  necessary  truths,  and  "  capable  of  demonstra- 
te 


362  DEMONSTRATIVE  REASONING 

tion,  like  the  truths  of  Geometry."  So  they  are,  if  viewed 
as  mere  Concepts,  not  necessarily  having  anything  cor- 
responding to  them  in  the  outward  universe.  But  if  re- 
garded as  Physical  Laws,  expressing  the  actual  phenom- 
ena of  real  things,  they  are  mere  educts  from  experience, 
can  be  reasoned  about  only  Inductively,  and  rest  solely 
upon  Probable  evidence. 

Deduction  is  not  a  happily  chosen  word  to  indicate  the 
characteristic  feature  of  reasoning  from  Universals  to  Par- 
ticulars, as  contradistinguished  from  Induction,  whereby  we 
reason  from  Particulars  to  Generals.  In  the  Syllogism 
which  expresses  the  Form  of  the  latter  process,  the  Con- 
clusion is  as  much  a  deduction  from  the  Premises,  as  in 
the  former  case.  We  may  speak  of  a  Law,  or  general  rule, 
as  deduced  from  several  individual  facts,  with  just  as  much 
propriety  as  of  facts  as  deduced  from  the  Law.  In  either 
case,  the  Conclusion  may  be  said  to  depend  upon  the  Prem- 
ises in  this  sense,  that  the  latter  authorize  us  to  proceed  to 
the  former.  But  it  is  a  mere  figure  of  speech,  and  not  a 
very  happy  one,  to  speak  of  the  Conclusion  as  so  involved 
in  the  Premises,  that  the  one  can  be  drawn  out  of,  or  de- 
duced, from  the  other.  The  process  is  rather  an  explica- 
tion of  what  was  previously  in  the  mind,  whereby  two  acts 
of  Thought  are  brought  into  harmony  with  each  other. 
The  Subsumption  either  includes  one  or  more  individuals 
in  a  class,  or  excludes  them  from  it;  and  the  Conclusion 
then  states  explicitly  what  is  virtually  or  implicitly  thought 
in  that  act  of  inclusion  or  exclusion.  The  process  of  rea- 
soning is  not  so  much  a  mode  of  evolving  a  new  truth,  as 
it  is  of  establishing  or  proving  an  old  one,  by  showing  how 
much  was  admitted  in  the  concession  of  the  two  Premises 
taken  together,  or  what  follows  from  the  act  of  bringing 
them  into  harmony.  The  Conclusion  is  not  authorized  by 
either  of  them  taken  singly. 

Hence  it  is  a  still  graver  mistake,  and  one  which  has 


AND   DEDUCTIVE  EVIDENCE.  363 

given  lise  to  much  misunderstanding,  to  speak  of  the  Con- 
clusion as  deduced  from  one  of  its  antecedents,  from  the 
Major  Premise  only.  A  Sumption  or  General  Rule  is  a 
necessary  part  of  every  Syllogism ;  but  it  does  not  by  any 
means  follow,  that  this  Rule  alone  implicitly  contains  all 
the  particular  Conclusions  which  are  ordinarily  said  to  be 
drawn  out  of  it.  The  Conclusion  is  drawn  in  accordance 
with  the  Rule,  and  the  latter  may,  in  one  sense,  be  said  to 
afford  a  proof  of  the  former,  inasmuch  as  it  evinces  that 
the  Conclusion,  if  the  truth  of  the  Minor  Premise  or  Sub- 
sumption  is  granted,  cannot  be  denied  without  overthrow- 
ing a  general  principle  the  truth  of  which  is  presupposed, 
as  resting  upon  the  evidence  either  of  Intuition,  or  of  a 
Primary  Law  of  Thought,  or  of  previous  Demonstration. 
In  one  sort  of  Immediate  Inference,  that  of  Subalterna- 
tion,  the  Premise  may  be  rightly  viewed  as  containing  the 
Conclusion,  as  a  whole  contains  one  of  its  parts,  and  the 
latter  may  therefore  be  held  to  be  deduced  from  the  for- 
mer. But  the  relation  between  the  Subalternans  and  the 
Subalternate  is  very  different  from  that  which  subsists  be- 
tween the  Sumption  and  the  Conclusion  in  a  case  of  Mediate 
Inference.  In  the  latter  case,  the  gist  of  the  reasoning 
does  not  depend  upon  any  Maxim  or  First  Principle,  but 
upon  the  discovery  of  a  Middle  Term,  with  which  both 
Terms  of  the  Conclusion  are  separately  compared.  This 
Middle  Term  is  the  name  of  a  Class,  and  the  new  truth 
which  is  developed  by  the  reasoning  consists  in  the  Sub- 
aumption  of  the  Subject  of  the  Conclusion  into  that  Class, 
and  the  consequent  discovery  that  it  possesses  all  the  attri- 
butes or  properties  which  are  connoted  by  its  Name.  For 
example :  —  the  geometer,  wishing  to  ascertain  the  size  of 
a  certain  angle,  finds  that  it  is  one  of  the  angles  of  an  equi- 
lateral triangle ;  this  is  the  Subsumption,  and  when  it  is 
accomplished,  the  discovery  is  really  made  and  the  problem 
solved,  for  the  Conclusion  that  the  angle  measures  60°  im- 


364  DEMONSTRATIVE  REASONING 

mediately  follows,  in  accordance  with  the  General  Truths 
already  demonstrated,  that  the  three  angles  of  an  equilat- 
eral triangle  are  equal  to  each  other,  and  that  their  sum  is 
180°.  But  no  manipulation,  no  analysis,  of  these  Truths 
previously  demonstrated  would  enable  him  to  evolve  from 
them,  without  the  aid  of  the  classification  given  in  the 
Minor  Premise,  the  measure  of  this  particular  angle. 
When  the  Sumption,  instead  of  being,  as  in  this  case,  a 
General  Theorem  previously  demonstrated,  happens  to  be 
one  of  those  Maxims  which  are  called  Axioms  in  Geome- 
try, it  is  still  more  evident  that  it  is  a  meagre  and  barren 
Rule,  from  which  no  fruitful  and  significant  Conclusion 
can  properly  be  deduced. 

I  accept,  then,  to  its  frill  extent,  the  doctrine  originally 
propounded  by  John  Locke,  and  adopted  and  defended  in 
our  own  day  by  Dugald  Stewart,  that  the  Axioms  of  Ge- 
ometry, and  the  other  very  general  maxims  which  are 
usually  considered  as  First  Principles  in  our  researches, 
"  are  not  the  foundations  on  which  any  of  the  Sciences  are 
built,  nor  at  all  useful  in  helping  men  forward  to  the  dis- 
covery of  unknown  truths."  If  Reasoning  were  an  organ  on 
of  discovery,  a  means  for  the  advancement  of  truth,  its  char- 
acteristic feature  would  appear  in  the  Subsumption,  which 
places  the  Subject  of  inquiry,  hitherto  anomalous,  or  of 
uncertain  classification,  under  a  Concept,  or,  what  is  the 
same  thing,  in  a  class,  the  attributes  of  which  are  known  ; 
and  the  proof  that  it  possesses  one  or  more  of  the  attributes 
of  that  class  then  appears  by  citing  the  General  Rule, 
which  is  the  Major  Premise.  In  other  words,  each  of  the 
two  Premises  in  a  Syllogism  has  its  own  appropriate  func- 
tion ;  the  Minor  announces  a  discovery,  a  new  truth,  which 
is  always  a  truth  of  classification,  and  the  Major  cites  an 
Axiom,  or  some  other  general  rule,  previously  well  known, 
which  proves  some  consequence  of  this  new  truth,  or  en- 
ables us  to  acquiesce,  with  more  or  less  confidence,  in  the 


AND  DEDUCTIVE  EVIDENCE.  365 

announcement  of  this  consequence.  If  the  Major  is  an 
Axiom  properly  so  called,  or  a  truth  previously  demon- 
strated, —  in  either  case,  having  absolute  universality  and 
certainty,  —  then  the  Conclusion,  if  the  Subsumption  is 
correct,  is  demonstrated  ;  but  if  it  is  merely  a  general  rule 
obtained  by  Induction  or  Analogy,  the  Conclusion  is  merely 
probable. 

The  correctness  of  this  analysis  will  appear,  I  think, 
from  an  examination  of  either  of  the  following  Syllogisms. 

1.  All  electricity  may  be  silently  drawn  off  from  any  charged 

body,  by  bringing  near  to  it  a  sharp-pointed  rod. 
Lightning  is  electricity. 
.*.  Lightning  may  be  so  discharged. 

2.  The  nervous  fluid  will  not  travel  along  a  tied  nerve. 
Electricity  will  travel  along  a  tied  nerve. 

.*.  Electricity  is  not  the  nervous  fluid. 

3.  All  alternate  angles  made  by  one  straight  line  cutting  two 

parallel  lines  are  equal. 
ABC  and  BCE  are  alternate  angles. 
.-.ABC  and  B  C  E  are  equal. 

4.  Things  which  are  equal  to  the  same  thing  are  equal  to  each 

other. 
A  B  and  B  C  are  each  equal  to  C  D. 
.*.  A  B  and  B  C  are  equal.  Jyf\^.^  -rows 

5.  Happiness  is  desirable.  [f**yr  T  T7  T?  T 
Virtue  is  happiness. 

.*.  Virtue  is  desirable.  ^^^4  7"  TT?ft 

It  is  evident  that  no  one  of  the  General  Rules  which 
form  the  Major  Premises  of  these  Syllogisms  can  be  "  at 
all  useful  in  helping  men  forward  to  the  discovery  of  un- 
known truths."  The  real  discovery  is  announced  in  the 
Minor  Premise,  and  the  connection  of  the  two  Premises  in 
one  act  of  reasoning  is  the  means  of  proving  the  Conclu- 
sion, and  of  assuming  it  into  its  proper  place  under  the 
General  Rule.     It  does  not  appear,  then,  that  Reasoning 


866  DEMONSTRATIVE  REASONING 

as  such,  or  as  an  act  of  Pure  Thought,  is  a  means  for  the 
advancement  of  knowledge.  This  doctrine,  indeed,  follows 
immediately  from  the  principles  that  have  been  already 
laid  down.  Reasoning  as  such  is  one  of  the  processes  of 
pure  Thought  which  determine  the  Form,  but  not  the  Mat- 
ter,  of  our  knowledge.  The  Matter  of  Thought  is  ob- 
tained by  Intuition,  —  by  observation  through  the  senses  or 
through  consciousness.  The  fact  or  truth  thus  discovered 
is  announced  in  the  Subsumption,  not  as  first  made  known 
by  it,  or  as  deduced  from  what  was  previously  known,  but 
in  order  to  be  proved  through  the  Reasoning  process ;  that 
is,  to  be  brought  into  harmony  with  our  previous  knowledge 
as  stated  in  the  Major  Premise,  and  that  the  same  conse- 
quences may  be  attributed  to  it  which  are  already  known  to 
follow  from  all  the  cases  included  under  that  general  state- 
ment. 

Accordingly,  what  Hamilton  remarks  of  the  whole  doc- 
trine of  Logic  may  be  applied  to  the  theory  of  Reasoning, 
which  is  but  one  of  the  departments  of  this  science.  We 
cite  again,  in  reference  to  one  of  the  parts,  what  has  been 
already  quoted  in  reference  to  the  whole.  "An  extension 
of  any  science  through  [pure  Reasoning]  is  absolutely  im- 
possible ;  for,  by  conforming  to  the  logical  canons,  we  ac- 
quire no  knowledge,  —  receive  nothing  new,  but  are  only 
enabled  to  render  what  is  already  obtained  more  intelligi- 
ble by  analysis  and  arrangement.  [Reasoning]  is  only  the 
negative  condition  of  truth.  To  attempt  by  mere  [Reason- 
ing] to  amplify  a  science,  is  an  absurdity  as  great  as  if  we 
should  attempt,  by  a  knowledge  of  the  grammatical  laws  of 
a  language,  to  discover  what  is  written  in  this  language, 
without  a  perusal  of  the  several  writings  themselves.  But 
though  [Reasoning]  cannot  extend,  cannot  amplify,  a  sci- 
ence by  the  discovery  of  new  facts,  it  is  not  to  be  supposed 
that  it  does  not  contribute  to  the  progress  of  science.  The 
progress  of  the  sciences  consists  not  merely  in  the  accumu- 


AND  DEDUCTIVE  EVIDENCE.  367 

lation  of  new  matter,  but  likewise  in  the  detection  of  the 
relations  subsisting  among  the  materials  accumulated ;  and 
the  reflective  abstraction  by  which  this  is  effected  "  must 
follow  the  laws  of  Reasoning. 

We  are  now  prepared  to  understand  and  appreciate 
Locke's  doctrine,  which  has  been  accepted  and  ably  sup- 
ported by  Mr.  Bailey  and  Mr.  J.  S.  Mill,  that  "the  imme- 
diate object  of  all  our  reasoning  and  knowledge  is  nothing 
but  particulars."  Locke  argues  that  "the  perception  of 
the  agreement  or  disagreement  of  our  particular  ideas  is 
the  whole  and  utmost  of  all  our  knowledge.  Universality 
is  but  accidental  to  it,  and  consists  only  in  this,  that  the 
particular  ideas  about  which  it  is  are  such  as  more  than 
one  particular  thing  can  correspond  with  and  be  repre- 
sented by.  But  the  perception  of  the  agreement  or  dis- 
agreement of  any  two  ideas  is  equally  clear  and  certain, 
whether  either,  or  both,  or  neither,  of  those  ideas  be  capa- 
ble of  representing  more  real  beings  than  one,  or  no."  * 
Mr.  Mill  says :  "  We  much  oftener  conclude  from  particu- 
lars to  particulars  directly,  than  through  the  intermediate 
agency  of  any  general  proposition.  We  are  constantly 
reasoning  from  ourselves  to  other  people,  or  from  one  per- 
son to  another,  without  giving  ourselves  the  trouble  to 
erect  our  observations  into  general  maxims  of  human  or 
external  nature."  f 

The  only  question  here  concerns  the  proper  use  of  words. 
The  process  of  comparing  one  individual  object  or  event 
with  another,  and  thereby  ascertaining  some  relation  be- 
tween them,  is  unquestionably  the  first  step  to  knowledge, 
and  the  only  means  of  enlarging  our  stock  of  knowledge. 
But  the  particular  fact  thus  learned  is  a  fact  of  observation^ 
not  of  reasoning.  Certainly  I  do  not  need  to  reason,  nor, 
in  the  strict  and  technical  sense,  to  think,  in  order  to  per 

*  Essay  on  Human  Understanding,  Book  IV.  Chap.  17,  §  8. 
f  System  of  Logic,  Book  II.  Chap.  3,  §  3. 


368  DEMONSTRATIVE   REASONING 

ceive  that  John  is  taller  than  William.  A  trute  perceives 
this  fact  as  well  as  I  do,  and  acts  upon  it,  as  in  distinguish- 
ing his  master.  Even  if  we  cany  the  process  one  step 
further,  and  form  a  Judgment,  by  subsuming  the  individual 
object  of  intuition  under  a  class,  through  perceiving  that  it 
affects  our  senses  just  as  some  other  objects  ranked  under 
that  class  have  done,  still  we  are  engaged  only  in  enlarging 
and  generalizing  our  knowledge,  and  not  in  reasoning  prop- 
erly so  called.  But  when  we  take  one  step  more,  and  pro- 
ceed to  attribute  certain  qualities  to  that  individual  thing, 
which  are  not  now  directly  perceived  in  it,  but  are  sup- 
posed to  exist  in  it,  because  we  have  noticed  them  in  other 
objects  of  the  same  class,  we  are  properly  said  to  reason ; 
the  act  is  one  of  Mediate  Inference.  But  this  act  does  not 
properly  enlarge  our  knowledge,  but  only  explicates  it,  by 
bringing  out  explicitly  into  Thought  what  was  already  vir- 
tually contained  in  it.  By  putting  an  object  into  a  class, 
we  have  already  virtually  attributed  to  it  all  the  qualities 
which  belong  to  that  class. 

This  doctrine  is  not  inconsistent  with  what  has  already 
been  maintained,  that  an  act  of  Reasoning  is  necessary  to 
enable  us  to  call  anything  by  its  appropriate  Common 
Name.  Mere  observation  cannot  teach  us  what  is  the 
proper  appellation  of  any  object  which  is  now  for  the  first 
time  perceived  ;  its  name  is  not  stamped  upon  it,  —  is  not 
one  of  its  qualities  directly  perceptible  either  by  sense  or 
consciousness.  But  by  the  joint  action  of  our  faculties  of 
perception  and  comparison,  we  are  made  aware  that  the 
new  object  resembles  a  certain  class  of  previously  known 
objects  in  all  the  particulars  which  are  connoted  by  tie 
name  of  that  class,  and  therefore,  that  the  object  may  be 
properly  subsumed  into  that  class,  and  called  by  its  name. 

The  doctrine  of  Locke  and  JV^ill,  then,  appears  true  to 
this  extent;  —  that  we  certainly  compare  one  individual 
thing  with  another,  and  only  by  such  comparison  can  dis- 


AND  DEDUCTIVE  EVIDENCE.  369 

coveries  be  made  and  knowledge  advanced.  But  that  sim- 
ple comparison,  and  the  consequent  perception  of  a  relation 
of  likeness  or  unlikeness,  is  not  an  act  of  reasoning.  We 
do  not,  in  the  technical  sense  of  the  term,  "  conclude  from 
particulars  to  particulars."  Before  this  particular  discov- 
ery can  be  made  available  for  the  purposes  of  Science,  — n 
before  it  can  be  brought  into  union  and  harmony  with  our 
previous  stock  of  knowledge,   an  act   of  Pure  Thought 

—  of  Mediate  Inference,  or  Reasoning  properly  so  called 

—  is  necessary.  We  must  become  aware  that  at  least  one 
of  the  two  Individuals  which  were  compared  together  is  a 
typical  specimen  or  representative  of  a  whole  Class,  and 
the  corresponding  Conclusion  must  be  reached,  that  the 
other  Individual  possesses  some  one  or  more  of  the  essen- 
tial attributes  of  that  Class.  To  advance  to  this  Conclu- 
sion is,  in  one  sense,  an  unimportant  step ;  for  it  contains 
nothing  new,  - —  it  does  not  increase  our  knowledge.  Hav- 
ing learned  the  individual  fact,  that  "  A  and  B  are  both 
equal  to  C,"  we  do  not  really  make  any  progress,  except  in 
the  way  of  systematizing  our  knowledge,  when  we  add  the 
very  obvious  corollary,  that  "they  are  equal  to  each  other," 
since  this  is  but  one  instance  under  the  General  Rule,  that 
"  all  which  are  equal  to  the  same  thing  are  equal  to  each 
other."  But  in  another  respect,  this  step  is  far  from  being 
unimportant.  Though  we  have  already  virtually  attributed 
all  the  qualities  of  the  class  to  the  individual  when  we  have 
included  that  individual  in  the  class,  so  that  the  technical 
Conclusion  only  draws  out  explicitly  what  was  already  im- 
plicitly thought,  a  new  act  of  classification  is  thus  com- 
pleted, and  the  memory  is  disburdened  of  particulars  by  an 
act  of  arranging  and  harmonizing  our  knowledge.  First 
to  bring  out  into  distinct  consciousness  the  truths  which 
are  already,  so  to  speak,  within  our  reach,  but  in  a  con- 
fused and  undeveloped  state,  and  then  to  place  them  under 
their  appropriate  heads  or  classes  in  a  methodized  system 

16*  I 


370  DEMONSTRATIVE  REASONING 

of  knowledge,  is  the  peculiar  office  of  Reasoning.  The 
Conclusion,  when  once  drawn,  is  obvious  enough ;  other- 
wise it  could  not  be  said  to  be  demonstratively  proved. 
But  far  the  greater  part  of  our  knowledge  exists  in  this 
half  latent  semi-developed  state ;  only  by  an  act  of  Rea- 
soning can  it  be  drawn  forth,  proved,  and  made  available 
for  use  in  further  inquiry.  In  respect  to  utility,  it  matters 
little  whether  our  stores  are  positively  enlarged,  or  our 
previous  acquisitions  are  developed,  systematized,  and  ren- 
dered more  efficient.  I  believe  that  no  new  truth  was 
ever  discovered  by  a  direct  process  of  pure  Reasoning; 
and,  on  the  other  hand,  that,  without  the  aids  and  appli- 
ances furnished  by  such  Reasoning,  no  progress  beyond 
the  most  elementary  steps  of  Science  would  have  been 
practicable.  Good  observers  discover  new  facts,  but  good 
reasoners  do  most  to  educate  and  instruct  mankind. 

Of  course,  the  fact  of  observation  on  which  the  Reason- 
ing is  based,  and  which  it  is  the  office  of  the  Reasoning  to 
develop,  is  not  necessarily  one  perceptible  by  sense.  The 
mere  thinker,  who,  by  some  lucky  chance  or  by  dint  of 
patient  reflection,  hits  upon  some  relation,  hitherto  unob- 
served, between  two  abstract  ideas,  is  just  as  much  a  dis- 
coverer, as  the  chemist  who  first  finds  that  a  metal  is  the 
basis  of  an  alkali ;  otherwise,  no  progress  could  be  made 
in  pure  mathematics  or  any  other  abstract  science.  The 
naked  fact,  that  the  square  upon  the  hypothenuse  of  a 
right-angled  triangle  is  equal  to  the  sum  of  the  squares 
on  the  two  other  sides,  was  observed  and  known  long  be- 
fore Pythagoras  first  succeeded  in  proving  it,  by  showing, 
through  a  series  of  Middle  Terms,  that  it  is  really  involved 
in  and  harmonizes  with  some  elementary  principles,  the 
whole  compass  and  meaning  of  which  had  not  before  been 
duly  developed.  The  fact  was  first  made  known  by  reflec- 
tive observation,  —  perhaps  by  sensible  experiment ;  but  it 
did  not  become  a  step  in  the  progress  of  Science  till  it  had 


AND   DEDUCTIVE  EVIDENCE.  371 

been  proved,  or  subsumed  under  some  broader  principles, 
and  thus  assigned  its  due  place  in  a  system  of  knowledge, 
by  an  act  of  pure  Reasoning. 

To  those  who  have  fully  considered  the  doctrine  which 
was  laid  down  at  the  commencement,  that  Logic  is  not  an 
organon  for  the  discovery  of  truth,  and  that  it  is  exclu- 
sively concerned  with  the  Form,  and  not  the  Matter,  of 
Thought,  this  discussion  may  seem  tr>  have  been  needlessly 
prolonged.  But  it  has  so  long  been  supposed  that  the 
admission  of  the  inapplicability  of  the  Syllogistic  process 
to  the  discovery  of  truth  was  tantamount  to  a  confession 
of  the  entire  inutility  of  the  science,  that  it  seemed  worth 
while,  even  at  the  expense  of  some  repetition,  to  prove 
that  this  supposition  was  wholly  groundless,  and  to  show 
precisely  what  is  the  utility  of  the  ends  to  which  mere 
Reasoning  is  subservient.  When  Mr.  Locke  says,  "  I  am 
apt  to  think  that  he  who  should  employ  all  the  force  of  his 
reason  only  in  brandishing  of  Syllogisms  will  discover  very 
little  of  that  mass  of  knowledge  which  lies  concealed  in  the 
secret  recesses  of  nature,"  we  have  a  right  to  answer,  in 
the  words  of  an  acute  logician,  Mr.  J.  Walker,  of  Dublin, 
that  "  he  expresses  himself  with  needless  caution.  Such  a 
man  will  certainly  not  discover  any  of  it.  And  if  any  im- 
agined that  the  mere  brandishing  of  Syllogisms  could  in- 
crease their  knowledge,  as  some  of  the  Schoolmen  seemed 
to  think,  they  were  indeed  very  absurd."  But  to  those 
who  consider  how  limited  the  range  of  human  knowledge 
would  be,  if  it  were  confined  to  isolated  facts  of  observation 
resulting  from  the  comparison  of  one  individual  thing  with 
another,  having  no  connection  with  each  other,  often  seem- 
ingly at  variance,  not  systematized,  not  summed  up  into 
general  timths,  and  hence  incapable  of  communication  by 
language,  it  will  be  evident  that,  without  the  capacity  and 
the  constant  exercise  of  Reasoning,  mankind  would  have 
advanced  but  little  beyond  the  condition  of  the  brutes. 


372  DEMONSTRATIVE   REASONING 

It  may  be  useful  to  enumerate  the  different  classes  of 
General  Rules  which  are  the  Major  Premises  of  all  Syllo- 
gisms, and,  as  such,  are  not  so  much  the  First  Principles 
whence  all  our  Conclusions  are  derived,  as  they  are  the 
Ultimate  Truths  in  which  all  Reasoning  terminates. 

1.  The  first  of  these  classes  consists  of  the  Primary 
Laws  of  Pure  Thought,  and  those  secondary  or  derivative 
maxims  into  which,  in  different  sciences  and  for  different 
purposes,  these  Primary  Laws  are  explicated.  In  Logic, 
as  we  have  seen,  both  the  supreme  Canons  of  Mediate  In- 
ference, such  as  the  Dictum  de  omni  et  nullo,  and  the  spe- 
cial Rules  of  various  sorts  of  Syllogisms,  are  all  resolvable, 
in  the  last  analysis,  into  these  Laws  of  Thought.  In  like 
manner,  the  Axioms  properly  so  called  of  Geometry,  that 
"  if  equals  are  added  to  equals,  the  wholes  are  equal,"  "  if 
equals  are  subtracted  from  equals,  the  remainders  are 
equal,"  &c,  are  only  varied  expressions,  explications,  or 
immediate  consequences,  of  the  Laws  of  Identity  and  Non 
contradiction. 

2.  The  foregoing  maxims  are  merely  analytic  or  explica- 
tive. The  next  class  consists  of  synthetic  or  ampliative 
Judgments.  These  are  necessary  intuitions  of  pure  rea- 
son, or  universal  truths  known  a  priori,  as  resulting  from 
the  constitution  of  the  mind  itself.  Such  are  the  Judgments, 
that  every  event  must  have  a  cause,  that  space  is  infinite, 
that  substance  underlies  all  material  attributes,  &c.  With 
these  I  am  inclined  to  rank  what  have  been  called  Axioms 
—  more  properly,  Assumptions  —  of  geometrical  science, 
as  they  are  propositions  which  the  geometer  must  assume 
to  be  true,  though  they  cannot  be  demonstrated ;  for  ex- 
ample, —  two  straight  lines  cannot  enclose  a  space ;  a 
straight  line  is  the  shortest  distance  between  two  points  ,• 
two  straight  lines  cut  by  a  third  line  at  equal  angles,  if 
produced,  will  never  meet. 

8.  We  also  reason  demonstratively  from  Definitions,  thai 


AND  DEDUCTIVE   EVIDENCE.  373 

is,  fra  n  explications  of  th?  Intension  of  any  C  oncepts  which 
we  see  fit  to  frame.  Of  course,  such  Judgments  are  purely 
analytic,  and  if  they  contain  no  unfounded  assumption, 
that  the  signification  thus  assigned  to  the  Names  of  the 
Concepts  is  that  which  is  usually  affixed  to  them  in  the 
common  use  of  language,  or  that  the  Marks  enumerated 
are  all  the  original  and  essential  qualities  of  the  real  things 
which  these  Names  denote,  the  Conclusions  at  which  we 
arrive  must  be  demonstratively  certain. 

4.  The  laws,  or  positive  precepts,  which  emanate  from 
any  sufficient  authority,  whether  human  or  divine.  These 
are  not  Judgments,  but  commands,  and,  as  they  are  to  be 
obeyed  at  all  hazards,  and  on  all  occasions,  the  only  ques- 
tion which  can  arise  respecting  them  concerns  their  inter- 
pretation. Of  this  nature  are  the  injunctions  of  conscience, 
the  laws  of  the  land,  and  the  commands  of  God,  as  made 
known  in  his  revealed  word.  Apart  from  any  doubt  which 
may  arise  concerning  the  signification  of  the  terms  in  which 
they  are  expressed,  any  Conclusion  legitimately  deduced 
from  such  commands  must  be  absolutely  valid,  since  uni- 
/ersality  is  of  the  very  nature  of  law. 

5.  Universal  propositions  previously  demonstrated. 

6.  Truths  of  generalization,  based  upon  observation  and 
Induction  or  Analogy.  These  are  true  only  to  the  extent 
of  our  experience,  which,  as  we  have  seen,  never  extends 
to  all  or  none.  Consequently,  these  propositions  rest  only 
upon  probable  evidence ;  and  though  such  evidence  be  suf- 
ficient for  moral  certainty,  they  are  not  available  for  Dem- 
onstration strictly  so  called.  We  may  assume  them  to 
be  universally  true,  and  upon  such  assumptions  may  rest 
perfectly  valid  syllogisms ;  but  the  Conclusion  in  such 
cases  will  have  no  other  or  higher  certainty  than  belongs 
to  the  Major  Premise. 

It  should  be  observed,  however,  that,  when  we  thus 
speak  of  merely  probable  evidence,  the  epithet  is  used  only 


374  DEMONSTRATIVE  REASONING 

in  its  technical  sense,  and  it  is  not  meant  that  we  have 
necessarily  less  confidence  in  it  than  in  mathematical  Dem- 
onstration. "  The  word  probable,  when  thus  used,"  says 
Dugald  Stewart,  "does  not  imply  any  deficiency  in  the 
proof,  but  only  marks  the  peculiar  nature  of  that  proof  as 
contradistinguished  from  another  species  of  evidence.  It 
is  opposed,  not  to  what  is  certain,  but  to  what  admits  of 
being  demonstrated  after  the  manner  of  mathematicians. 
This  differs  widely  from  the  meaning  annexed  to  the  same 
word  in  popular  discourse  ;  according  to  which,  whatever 
event  is  said  to  be  probable  is  understood  to  be  expected 
with  some  degree  of  doubt."  Perhaps  the  clearest  distinc- 
tion between  Demonstrative  and  Probable  evidence  consists 
in  the  fact,  that  the  former  does  not  admit  of  degrees,  as  a 
proposition  is  either  demonstrated  absolutely,  or  not  at  all ; 
while  the  latter  may  exist  in  any  degree,  from  the  faintest 
shade  of  probability  up  to  moral  certainty. 

This  seems  the  proper  place  for  the  explanation  of 
the  technical  terms,  or  Second  Intentions  of  Judgments, 
that  are  used  in  the  construction  of  Science.  Most  of 
these,  however,  are  of  infrequent  occurrence,  except  in  the 
mathematical  sciences.  All  propositions  are  either  Theo- 
retical or  Practical ;  —  the  former  are  purely  speculative, 
the  truths  which  they  enounce  being  merely  objects  of  con- 
templation by  the  mind,  as  having  no  reference  to  action 
or  conduct ;  the  latter  have  regard  to  something  which  is 
to  be  done  or  omitted,  to  some  performance  or  mode  of 
procedure.  Propositions  are  also  said  to  be  demonstrable, 
if  they  require  or  admit  of  proof ;  they  are  indemonstrable, 
if  they  are  self-evident,  or  intuitively  known. 

An  indemonstrable  judgment,  if  theoretical,  is  called  an 
Axiom;  if  practical,  it  is  styled  a  Postulate.  A  demon- 
strable judgment,  or  one  which  is  announced  as  needing 
proof,  if  theoretical,  is  called  a  Theorem;  if  practical,  it  is 
a  Problem,     A  Thesis  coincides  very  nearly  with  a  Theo- 


AND  DEDUC1IVE  EVIDENCE.  375 

rem ;  it  is  a  judgment  proposed  for  discussion  and  proof. 
A  Corollary  is  a  truth  announced  as  an  immediate  conse- 
quence or  collateral  result  of  another  judgment  that  has 
just  been  proved,  and  therefore  as  not  needing  any  sepa- 
rate proof  for  itself.  A  Judgment  which  does  not  properly 
belong  to  the  science  in  which  it  appears,  but  is  borrowed 
from  some  other,  is  called  a  Lemma;  one  which  merely 
illustrates  the  science,  but  is  not  an  integral  part  of  it,  is  a 
Scholion.  An  Hypothesis  is  a  judgment  not  known  to  be 
true,  but  accepted  for  the  time  as  a  provisional  explanation 
of  some  phenomena,  and  as  liable  to  be  modified  or  rejected 
altogether  on  the  production  of  further  evidence.  A  The- 
ory, sometimes  incorrectly  used  as  a  synonyme  for  Hypothe- 
sis, is  a  comprehensive  and  methodical  arrangement  of 
some  large  group  of  phenomena  under  their  supposed 
Causes  and  Laws,  offered  as  at  least  a  provisional  accoant 
of  them  and  mode  of  reducing  them  to  system.  "  Theoria- 
rum  vires"  says  Bacon,  "  arctd  et  quasi  se  mutuo  sustinente 
partium  adaptatione,  qud  quasi  in  orbem  cohatrtnt,  firman- 
tur." 


376  INDUCTION  AND   ANALOGY 


CHAPTER    XII. 

INDUCTION  AND  ANALOGY. 

ANY  act  of  Reasoning  strictly  so  called  presupposes  the 
universality  of  its  Sumption  or  Major  Premise.  If  I 
am  not  absolutely  certain  that  all  A  are  B,  then,  though 
the  Subsumption  that  C  is  A  be  undoubtedly  true,  I  can- 
not be  sure  that  C  is  B. 

Now  it  has  been  repeatedly  proved,  that  universal  Judg- 
ments cannot  be  derived  from  mere  experience,  which  is 
competent  to  pronounce  upon  some,  or  many,  but  never 
upon  all,  or  none.  But  as  we  cannot  have  any  knowledge 
of  real  things,  or  actual  existences,  except  by  means  of 
experience,  it  follows  that  such  things  are  not  objects  of 
Reasoning  in  the  proper  sense  of  the  term,  —  that  is, 
of  Demonstrative  Reasoning,  in  which  the  Conclusion  is 
accepted  with  absolute  certainty.  From  the  enumeration 
which  has  just  been  made,  it  appears  that,  with  the  unim- 
portant exceptions  of  legal  precepts  and  a  few  truths  known 
a  priori,  all  Major  Premises  must  be  either  mere  analytic 
judgments  obtained  by  explicating  our  own  abstract  con- 
ceptions, or  general  rules  that  are  true  only  to  the  extent 
of  our  experience.  We  may  assume  such  rules  to  be  uni- 
versally true,  and  the  Reasoning  will  then  become  perfect 
or  Demonstrative  in  Form ;  but  as  the  Conclusion  can 
never  be  purged  from  the  shade  of  uncertainty  thrown 
upon  it  by  the  imperfect  evidence  of  the  universality  of 
its  Major  Premise,  such  Reasoning  is  rightly  considered  as 
merely  'probable  or  contingent.     We  may  suppose,  also,  that 


INDUCTION  AND  ANALOGY.  377 

the  real  existences  perfectly  correspond  to  the  abstract  con- 
ceptions that  we  have  formed  of  them,  and,  in  this  way, 
may  seem  to  obtain  absolute  Conclusions  about  matters  of 
fact.  This  is  commonly  said  to  be  reasoning  from  hypoth- 
eses ;  but  just  so  far  as  such  reasoning  is  Demonstrative,  it 
concerns  only  the  Concept,  which  cannot  be  more  than  an 
imperfect  representation  of  the  reality. 

For  illustration,  I  borrow  from  Mr.  Bailey's  "  Theory 
of  Reasoning,"  page  2,  the  following  examples  of  Probable 
or  contingent  Reasoning. 

1.  "  I  am  walking,  I  will  suppose,  on  the  sea-shore,  and,  perceiv- 

ing a  quantity  of  sea-weed  lying  on  the  beach,  while  the 
water  is  at  the  moment  a  quarter  of  a  mile  from  it,  I  con- 
clude that  the  tide  has  ebbed,  and  left  the  weed  where  I 
perceive  it  lying." 

2.  "  I  notice  the  print  of  a  small  foot  on  the  sand,  and  I  feel 

pretty  sure  that  it  was  made  by  a  child." 

Each  of  these  instances  may  be  resolved  into  the  Form 
of  perfect  or  Demonstrative  Reasoning,  and  it  will  then  be 
Been  that  the  uncertainty  which  attaches  to  the  Conclusion 
arises  solely  from  the  doubt,  which  experience,  however 
often  repeated,  is  incompetent  to  remove,  as  to  the  abso- 
lute universality  of  the  Major  Premise. 

1.  All  sea-weed  found  within  the  space  usually  covered  by  the 

sea  at  high  water  must  have  been  left  there  by  the  ebbing 
of  the  tide ; 
This  bunch  of  sea-weed  was  so  found ;  therefore,  &c. 

2.  No  small  foot-shaped  imprint  on  the  sand  can  have  been   .eft 

by  anything  else  than  the  foot  of  a  child ; 
This  is  a  small  foot-shaped  imprint  on  the  sand ;  therefore,  &c. 

"  In  these  several  cases,"  says  Mr.  Bailey,  "  my  mind  is 
determined  by  the  sight  of  present  phenomena,  conjoined 
with  knowledge  previously  acquired,  to  believe  something 
which  I  do  not  actually  perceive  through  the  organs  of 


878  INDUCTION  AND   ANALOGY. 

sense ;  —  something  past,  something  future,  or  something 
distant ;  or,  in  other  words,  to  believe  that  some  event  has 
happened,  will  happen,  or  is  happening,  although  beyond 
the  sphere  of  my  observation."  In  short,  it  is  an  attempt 
to  make  the  Thinking  faculty  do  the  work  of  the  Percep- 
tive faculty ;  to  gain  a  knowledge  of  an  external  fact  by  a 
mere  process  of  Thought,  instead  of  acquiring  it  by  obser- 
vation through  the  senses.  Such  an  attempt  can  have  but 
imperfect  success  ;  its  result  is  not  properly  denominated 
knowledge,  but  belief,  or  opinion.  The  inference  is  rightly 
said  to  rest  upon  moral,  or  probable,  evidence. 

It  is  contended  by  some,  that  the  mind  actually  rests 
such  inferences  upon  the  amount  of  evidence  which  has 
really  been  collected,  though  conscious  that  it  is  incom- 
plete, and  does  not  go  through  the  Form  of  assuming  a 
Major  Premise  which  is  absolutely  universal,  and  which, 
if  we  were  only  sure  that  it  was  well  founded,  would  ren- 
der the  Conclusion  certain.  Thus,  to  recur  to  one  of  the 
instances  just  cited,  Mr.  Bailey  argues  that  the  Premise 
from  which  the  mind  actually  draws  the  inference  is  what 
he  terms  the  Collective  Fact,  viz.  that,  in  all  the  cases  which 
I  have  ever  observed  or  heard  of,  all  sea-weed  so  found  has 
been  left  by  the  tide,  —  and  not  the  G-eneral  Law,  an- 
nounced without  this  limitation,  which  affirms  as  much  ab- 
solutely of  all  sea-weed  so  found.  He  maintains  that  the 
General  Law  itself,  just  as  much  as  the  particular  case  in 
question,  is  an  inference  from  the  Collective  Fact.  To 
rest  the  inference  respecting  the  individual  case  upon  the 
General  Law,  does  not  make  the  Conclusion  a  whit  more 
probable,  than  to  rest  it  upon  the  Collective  Fact  on  which 
this  General  Law  itself  is  founded. 

Perhaps  the  question  is  one  which  does  not  merit  much 
discussion.  Obviously  it  matters  not  whether  the  mind,  in 
seeking  for  competent  proof  of  this  particular  inference, 
proceeds  by  throwing  what  evidence  it  possesses  into  the 


INDUCTION  AND  ANALOGY.  379 

Form  of  perfect  or  Demonstrative  reasoning,  through  the 
assumption  of  a  Major  Premise  which  is  not  free  from 
doubt ;  or  whether  it  forbears  any  undue  assumption  in  the 
Premises,  and  adopts  a  process  of  inference  which  is  con- 
fessedly imperfect  even  in  Form.  Taking  a  doubtful  asser- 
tion for  a  Premise,  it  thus  preserves  the  Form  of  valid 
reasoning. 

All  men  are  fallible ; 

The  author  of  this  book  is  a  man ; 

Therefore  the  author  of  this  book  is  fallible. 

Restrict  the  statement  in  the  Major  Premise,  so  that  it 
shall  express  no  more  than  what  is  known  to  be  true,  and 
the  Reasoning  thus  becomes  invalid  through  an  undistrib- 
uted Middle. 

All  men,  so  far  as  observation  has  extended,  have  been  fallible  ; 
Therefore  this  author  is  fallible. 

As  a  fact,  however,  I  believe  the  first  of  these  forms  is 
much  more  frequently  in  use.  For  proof  in  any  particular 
case,  we  usually  refer  to  a  Law  of  Nature,  the  universal- 
ity of  which  is  expressed  with  as  little  hesitation  as  if  it 
were  a  Law  of  Thought.  The  usual  form  of  Enthymeme 
employed  is  the  following:  —  This  bit  of  iron  will  melt, 
because  all  iron  is  fusible ;  This  water  will  boil  at  212°, 
because  water  always  boils  at  that  temperature ;  These 
men  must  die,  for  all  human  beings  are  mortal.  In  truth, 
with  the  exception  of  those  who  have  made  a  special  study 
of  the  theory  of  Reasoning,  nobody  thinks  of  restricting 
the  universality  of  such  statements  by  the  qualifying  clause, 
"  so  far  as  has  been  observed,"  or  "  according  to  all  known 
experience."  And  it  is  not  mere  carelessness  in  the  use 
of  language,  or  the  proneness  to  exaggeration  which  has 
already  been  pointed  out  for  censure,  that  causes  such 
statements  to  be  made  without  their  proper  limit?  tions. 
Very  few  are  conscious,  even  after  reflection,  that  there 


380  INDUCTION  AND  ANALOGY. 

is  an}'-  exaggeration  in  the  case;  and  there  is  none,  except 
what  is  implied  by  adopting  the  Form,  without  the  sub- 
stance, of  Demonstrative  Reasoning. 

Induction  and  Analogy  are  the  two  processes  of  thought 
by  which  we  endeavor  to  make  our  Judgments  about  whole 
classes  of  real  objects,  or  actual  existences,  approximate  the 
absolute  certainty  and  universality  of  our  Judgments  about 
abstract  conceptions.  Hence  they  are,  what  Pure  Reason- 
ing is  not,  organa  for  the  discovery  of  truth  and  the  actual 
advancement  of  knowledge.  But  just  so  far  as  they  are 
means  to  these  ends,  they  lose  the  character  of  Pure  or 
Demonstrative  Reasoning;  the  Syllogisms  to  which  they 
are  reducible  are  faulty  either  in  Matter,  as  having  a 
Major  Premise  the  universality  of  which  is  merely  proba- 
ble, or  in  Form,  as  containing  an  undistributed  Middle. 
The  question  whether  they  are  entitled  to  be  called  Rea- 
soning is  hardly  worth  discussing  here,  as  it  concerns  only 
the  use  of  words.  Logical  or  Demonstrative  Reasoning 
they  are  not ;  but  they  may  be  denominated  Probable 
Reasoning,  or  Philosophical  Presumptions. 

It  should  be  mentioned,  however,  that  what  may  be 
termed  Logical  Induction,  the  plena  enumeratio  of  the 
logicians,  which  deduces  a  General  Rule  from  what  is 
known  to  be  true  of  every  individual  in  the  class,  belong? 
to  Pure  Reasoning  strictly  so  called.  Conclusions  drawn 
from  such  Premises  as  the  following,  are  Demonstrative  01 
absolutely  certain  ;  but  these  only  generalize  our  knowl- 
edge, or  alter  its  expression ;  they  do  not  enlarge  it. 

Mercury,  Venus,  the  Earth,  &c.  are  all  the  Planets. 
Peter,  James,  John,  Matthew,  &c.  are  all  the  Apostles. 

This  mode  of  Reasoning  has  already  been  analyzed ;  bul 
it  is  not  what  is  understood  by  Induction  in  the  processes 
of  Science.  Logical  Induction  concludes  from  each  one  to 
all;  Induction  properly  so  called  concerns  the  Matter  of 
Thought,  and  concludes  from  some  to  all. 


INDUCTION  AND  ANALOGY.  381 

The  difference  between  Induction  and  Analogy  has  been 
clearly  stated  and  illustrated  by  Kant.  In  order  to  enlarge 
our  knowledge  beyond  the  bounds  of  experience,  we  must 
either  conclude  from  many  things  to  all  others  of  the  same 
Species,  which  is  Induction  ;  or  we  must  conclude  from 
the  known  agreement  of  two  things  in  several  qualities, 
that  they  agree  also  in  some  other  quality  which  is  not 
directly  known.  In  our  progress  from  the  Particular  to 
the  General,  Induction  proceeds  upon  the  principle,  that 
what  certainly  belongs  to  many  Individuals  of  the  same  kind, 
also  probably  belongs  to  all  the  other  Individuals  of  that  hind; 
the  principle  of  Analogy  is,  that,  if  two  things  agree  in  many 
respects,  they  probably  agree  also  in  some  other  respect.  Be- 
cause some  one  quality  exists  in  many  things,  therefore  it 
exists  in  all  of  the  same  kind ;  this  is  Induction.  Because 
many  qualities  in  this  are  the  same  as  in  that,  therefore  one 
other  quality  in  this  resembles  that ;  this  is  Analogy.  In 
other  words,  Induction  concludes  from  one  in  many  to  the 
others,  by  way  of  Extension ;  Analogy,  from  many  in  one 
to  the  others,  by  way  of  Intension. 

The  following  are  instances  of  Induction  :  — 

1.  In  many  cases  in  which  water  has  been  analyzed,  it 
has  been  found  to  consist  solely  of  oxygen  and  hydrogen ; 
therefore,  all  water  is  made  up  from  these  two  elements. 

2.  Very  many  animals  have  been  examined,  and  these, 
without  a  single  exception,  have  been  found  to  possess  a 
nervous  system  ;  therefore,  all  animals  have  a  nervous 
system. 

3.  Most  bodies  expand  in  bulk,  if  heated ;  therefore, 
heat  always  produces  expansion,  if  it  be  not  counteracted 
by  some  other  cause. 

The  following  are  instances  of  Analogy  :  — 
1.  The  planets  Venus  and  Mars  resemble  the  earth  in 
many  respects,  as  in  size,  density,  time  of  rotation  on  the 
axis,  distance  from  the  sun,  receiving  light  and  heat  from 


382  INDUCTION  AND  ANALOGY. 

it,  &c. ;  therefore,  they  probably  resemble  it  in  one  other 
respect,  in  being  inhabited  by  living  beings. 

2.  Fossil  skeletons  that  are  found  in  the  rocks  bear  a 
close  resemblance  in  very  many  respects  to  the  skeletons 
which,  as  we  know,  once  belonged  to  recently  living  ani- 
mals ;  therefore,  they  resemble  them  in  one  other  respect, 
in  that  these  fossils  are  the  remains  of  animals  which  were 
formerly  living  upon  the  earth. 

3.  In  many  respects,  as  in  complexity  of  parts,  nice  ad- 
justment and  mutual  dependence  of  these  parts  one  upon 
another,  delicacy  of  finish,  symmetry,  and  adaptation  to 
many  useful  ends,  the  human  hand  resembles  some  inge- 
nious machines,  which  we  know  to  have  been  contrived  and 
fashioned  by  the  exercise  of  mind ;  therefore  the  hand  was 
so  contrived  and  fashioned. 

4.  The  argument  of  Origen  and  Bishop  Butler  is,  that 
if  the  Scriptures  and  the  constitution  of  Nature  are  alike  in 
this  respect,  that  they  proceeded  from  the  same  Author, 
we  may  well  expect  to  find  the  same  difficulties  in  the  for- 
mer as  are  found  in  the  latter. 

It  is  plain  that  what  is  here  called  Analogy  is  the  same 
mental  process  which  is  described  and  analyzed  by  Aris- 
totle as  "  reasoning  from  Example."  He  gives  the  follow- 
ing as  an  instance  of  this  sort  of  argument.  If  we  would 
prove  that  it  is  not  expedient  for  the  Athenians  to  make 
war  upon  the  Thebans,  who  are  their  neighbors,  we  may 
reason  from  the  analogous  case,  that  the  war  against  the 
Phoceans,  who  were  their  neighbors,  was  fatal  to  the  The- 
bans. He  says  that  Example  is  not  founded,  like  Syllo- 
gism, upon  the  relation  of  the  whole  to  its  parts,  nor,  like 
Induction,  upon  the  relation  of  the  parts  to  the  whole,  but 
upon  the  relation  of  one  part  to  another,  because  the  one 
is  more  perfectly  known  than  that  other.  The  Aristotelic 
Induction  proceeds  from  all  the  individual  cases,  while  Ex- 
ample is  founded  only  upon  some  of  them,  perhaps,  as 
above,  upon  a  single  instance. 


INDUCTION  AND  ANALOGY.  383 

Comparatively  little  need  be  said  of  Analogy,  as  the  Con- 
clusions to  which  it  leads  are  evidently  not  Demonstrative, 
but  merely  Probable.  Strictly  speaking,  there  is  no  proof 
whatever,  because  two  things  resemble  each  other,  how- 
ever nearly,  or  in  however  many  respects,  that  the  resem- 
blance extends  to  a  single  point  other  than  what  has  been 
actually  observed.  The  existence  of  one  quality,  it  is  true, 
may  be  necessarily  implied  in  that  of  another,  either  by  the 
Laws  of  Thought,  or  by  the  a  priori  laws  of  the  human 
mind ;  as  one  geometrical  property  of  a  body  may  be  de- 
duced from  another,  or  as  its  divisibility  may  be  inferred 
from  its  extension.  This  is  Demonstrative  Reasoning,  but  it 
is  merely  explicating  our  knowledge,  and  not  directly  add- 
ing to  it ;  and  certainly  it  is  not  reasoning  from  Analogy, 
which  proceeds  from  similarity  in  some  respects  to  similar- 
ity in  one  other,  or  in  many  others.  Analogical  conclu- 
sions may  have  any  degree  of  probability,  varying  from  a 
merely  permissible  hypothesis  up  to  what  may  fairly  be 
called  moral  certainty.  Because  this  kind  of  inference  is 
often  greatly  abused,  for  some  degree  of  resemblance  may 
often  be  detected  between  two  things  apparently  most  dis- 
similar, —  skill  in  such  detection,  when  the  inference  is 
ludicrously  improbable,  constituting  wit,  —  I  am  inclined 
to  think  that  the  force  of  which  it  is  susceptible  is  generally 
underrated.  *  Slight  Analogies  are  worth  nothing,  except 
to  show  that  the  coexistence  of  two  or  more  qualities  is 
barely  possible,  no  belief  whatever  being  justly  created  that 
it  is  probable.  On  the  other  hand,  the  Analogy  may  be 
so  perfect  that  the  Conclusion  founded  upon  it  may  be  ac- 
cepted with  as  full  faith  as  if  it  rested  upon  an  extensive 
and  cautious  Induction,  with  which,  indeed,  it  is  frequently 
confounded. 

To  recur  to  the  instances  just  cited.  The  supposition 
that  the  other  planets  are  inhabited  rests  upon  an  Analogy 
which  is  so  faint  and  imperfect,  that  it  does  not  afford  suffi- 


384  INDUCTION   AND   ANALOGY. 

cient  ground  for  making  up  any  opinion  on  the  subject, 
either  for  or  against  the  hypothesis.  The  resemblance  is 
but  slight,  even  in  the  few  particulars  that  are  cited ;  and 
we  have  no  evidence  that  there  is  any  similarity  whatevei 
in  a  vast  number  of  other  respects,  many  of  which  are 
essential  to  the  existence  of  life  under  any  of  the  forms 
with  which  we  are  acquainted.  On  the  other  hand,  the 
Analogy  between  the  skeletons  that  exist  only  in  a  fossil 
state,  and  those  of  animals  now  living,  is  so  broad  and  per- 
fect, that  a  man's  sanity  or  sincerity  would  be  questioned 
who  should  affect  to  doubt  that  the  former  also  once  walked 
the  earth  or  swam  in  the  seas.  These  fossils  do  not  differ 
more  from  the  extant  types  than  many  of  the  latter  do 
from  each  other,  while  in  the  numberless  points  of  Analogy 
the  resemblance  is  perfect.  And  the  conclusion  in  the 
third  case,  founded  upon  the  Analogy  between  the  human 
hand  and  a  contrivance  of  man's  device,  is  still  more  indis- 
putable. If,  without  the  aid  of  mind,  without  foresight  or 
design,  the  mere  fortuitous  concourse  of  atoms,  in  the  lapse 
of  a  past  eternity,  could  have  formed  a  living  tree,  fish,  or 
elephant,  then,  we  say,  that  same  rudderless  and  purpose- 
less crowd  of  primeval  atoms,  in  the  lapse  of  a  past  eter- 
nity, could  have  formed,  what  is  much  easier,  &  fossil  tree, 
fish,  or  elephant.  We  are  here  pointing  out  the  analogous 
character  of  two  arguments,  each  founded  upon  Analogy, 
but  pointing  to  different  Conclusions  ;  and  we  find  the  re- 
semblance between  them  so  perfect,  that  it  is  impossible  to 
maintain  the  validity  of  the  Conclusion  in  the  former  case, 
and  deny  it  in  the  latter. 

The  definition  which  is  ordinarily  given  of  Analogy,  that 
it  means  proportion,  or  a  similarity  of  relations,  does  not 
differ  from  the  one  here  propounded.  Thus,  it  is  said, 
when  we  affirm  the  relation  of  the  fins  of  a  fish  to  the 
water  to  be  the  same  [similar]  to  that  of  the  wings  of  a 
bird  to  the  air,  that  we  are  judging  from  Analogy.     So  we 


INDUCTION  AND  ANALOGY.  385 

are ;  we  are  pointing  out  what  is  perhaps  an  unexpected 
resemblance  amid  apparent  diversity.  However  unlike 
fins  are  to  wings,  we  still  pronounce  that  they  agree  in  this, 
the  adaptation  of  the  former  to  the  animal's  motion  through 
the  water  being  very  similar  to  the  fitness  of  the  latter  to 
effect  motion  through  the  air.  From  this  equality  of  fit- 
ness for  corresponding  purposes,  we  reason  analogically  that, 
if  one  was  contrived  by  intelligence,  the  other  was  also. 

Induction,  says  Mr.  Mill,  u  may  be  summarily  defined  as 
Generalization  from  Experience.  It  consists  in  inferring 
from  some  individual  instances  in  which  a  phenomenon  is 
observed  to  occur,  that  it  occurs  in  all  instances  of  a  cer- 
tain class  ;  namely,  in  all  which  resemble  the  former  in 
what  are  regarded  as  the  material  circumstances."  This 
last  qualification  is  an  important  one,  and  has  not  received 
sufficient  notice  from  those  who  have  speculated  upon  the 
theory  of  Induction.  The  process  would  be  invalid  and 
nugatory,  if  we  did  not  presuppose  the  correctness  of  the  pre- 
ceding Classifications  that  have  been  formed  of  the  objects  of 
Science.  A  conclusion  from  some  to  all  would  not  hold, 
would  not  have  even  the  slightest  shade  of  probability,  if  it 
were  applied  to  a  Class  formed  of  the  objects  now  contained 
in  this  room,  or  of  those  embraced  within  my  present  field 
of  vision,  or  of  things  having  no  common  attribute  except 
that  they  are  of  the  same  color,  or  the  same  size.  But 
such  a  conclusion  becomes  extremely  probable,  even  mor- 
ally certain,  when  applied  to  a  Class,  like  that  of  metals 
or  stars,  having  many  common  characteristics  which  are 
definite  and  peculiar.  Thus,  having  ascertained  of  only 
♦wo  metals,  iron  and  copper,  that  they  are  conductors  of 
electricity,  it  would  be  a  tolerably  safe  Induction,  that 
all  metals  are  such  conductors.  Having  found  that  one 
thunder-cloud  was  electrical,  Franklin  at  once  safely  leaped 
to  the  conclusion,  that  all  such  clouds  had  that  property. 
We  have  already  seen  that  t^e  Classifications  formed  of  the 
17  x 


386  INDUCTION  AND  ANALOGY. 

innumerable  objects  of  thought  cannot  be  arbitrary,  but 
must  be  framed  to  embrace  as  many  common  or  similar  t 
elements  as  possible.  The  numberless  properties  of  a 
geometric  figure  can  be  deduced  by  necessary  inference 
from  the  one  or  two  leading  properties  of  it  which  are 
selected  to  form  its  Definition.  And  the  hope  always  is, 
in  forming  a  Classification  of  real  objects  or  events  in  Na- 
ture, to  hit  upon  some  attribute  as  the  basis  of  the  arrange- 
ment with  which  all  the  other  qualities  of  it  are  connected 
by  some  necessary,  though  to  us  invisible,  tie. 

This  appears  to  afford  the  solution  of  a  problem  which 
has  puzzled  many  inquirers ;  —  how  it  is,  that  we  often 
safely  frame  an  Induction  from  a  single  instance,  while,  in 
other  cases,  the  conclusion  is  precarious,  though  supported 
by  a  multitude  of  affirmative  examples.  Thus,  the  chem- 
ist, having  discovered  a  new  metal,  ascertains  by  a  single 
experiment  its  specific  gravity,  degree  of  hardness,  tough- 
ness, &c,  and  then  safely  concludes  that  every  other  speci- 
men of  the  metal,  which  may  afterwards  be  obtained,  will 
be  found  to  possess  these  qualities  in  the  same  degree.  On 
the  other  hand,  a  multitude  of  instances  of  recovery  from  a 
specific  disease  after  the  administration  of  a  particular  drug 
are  insufficient  to  establish  the  universal  efficacy  of  the  med- 
cine  in  what  appear  to  be  similar  cases.  In  Meteorology, 
also,  and  in  the  several  branches  of  Natural  History,  though 
the  Induction  may  be  very  extensive,  and  conducted  with 
all  possible  caution,  the  general  conclusions  have  only  that 
low  degree  of  probability  which  is  indicated  by  calling 
them  empirical  laws.  The  reason  of  this  difference  evi- 
dently is,  that  the  Classifications  in  the  science  of  Chemistry 
approach  very  nearly  to  perfection,  the  qualities  determina- 
ble by  chemical  analysis  being  definite,  strongly  marked, 
and  constant  in  their  forms  of  combination  with  each  other ; 
while  Medicine,  Meteorology,  and  Natural  History  are, 
and  probably  must  ever  remain,  sciences  very  imperfect  in 


INDUCTION  AND  ANALOGY.  387 

Classification,  as  the  objects  with  which  they  are  concerned 
have  an  indefinite  multitude  of  ill-determined  attributes, 
shaded  into  each  other  by  imperceptible  degrees,  and  com- 
bined in  the  most  irregular  manner.  The  lines,  and  even 
the  principles,  of  division  of  the  objects  of  these  sciences  are 
merely  provisional,  and  are  frequently  changed,  so  as  to 
adapt  them  to  the  progress  of  observation,  or  in  the  hope 
of  hitting  upon  some  qualities  which  may  be  found  in  more 
constant  relations  with  the  other  leading  properties  than 
those  which  have  hitherto  formed  the  basis  of  the  Classifica- 
tion. Of  course,  the  Induction  becomes  extremely  preca- 
rious, when  we  are  not  sure  that  the  instances  over  which 
it  extends  agree  with  each  other  in  all  material  circum- 
stances. 

It  is  evident,  moreover,  that  the  smaller  the  Class  is,  01 
the  nearer  that  it  comes  to  an  Infima  Species,  the  stronger 
is  our  assurance  that,  in  reference  to  this  Class,  the  conclu- 
sion from  some  to  all  will  hold  good.  The  Induction  is 
safer,  for  instance,  from  some  to  all  lumps  of  iron,  than 
from  some  to  all  metals ;  and  it  is  still  more  certain  in  ref- 
erence to  all  specimens  of  one  kind  of  iron,  wrought  or 
malleable,  than  with  respect  to  all  sorts  of  that  metal.  As 
the  Extension  and  Intension  of  the  Class-name  are  in  in- 
verse ratio  to  each  other,  that  is,  as  the  number  of  attri- 
butes connoted  is  greater  in  proportion  as  the  number  of 
objects  denoted  is  less,  the  similarity  of  the  members  of  the 
Class  to  each  other  is  increased  as  the  number  of  those, 
members  is  diminished ;  and  the  greater  the  similarity,  the 
safer  the  Induction,  because  it  is  then  more  probable  that 
the  resemblance  extends  to  the  material  or  essential  cir- 
cumstances. As  the  Intension  is  greater,  the  Induction  is 
founded  upon  a  larger  number  of  qualities,  that  is,  upon  a 
more  perfect  resemblance ;  and  as  the  Extension  is  less, 
the  Induction  extends  to  fewer  objects,  and  is  therefore 
more  likely  to  be  well  founded.     The  gap  between  some 


388  INDUCTION   AND   ANALOGY. 

and  all  is  not  so  great,  when  even  all  denotes  onlj  a  few 
We  cannot  safely  reason,  from  the  process  of  treatment 
which  has  been  effectual  in  one  case  of  fever,  to  the  effi- 
ciency of  the  same  treatment  in  any  other  instance,  merely 
because  the  symptoms  of  no  one  fever-stricken  patient  have 
anything  more  than  a  general  resemblance  to  those  of  an- 
other; and  the  internal  peculiarities  of  the  malady,  of 
which  the  outward  symptoms  are  only  the  faint  and  easily 
mistakable  indications,  are  still  more  unlike. 

Thus  much,  however,  is  certain,  that  if  the  Classification 
is  correct,  if  the  cases  brought  together  are  really  parallel 
in  all  the  essential  circumstances,  —  and  we  must  presup- 
pose as  much  as  this  before  we  can  reason  from  Induction 
at  all,  —  then  we  firmly  believe,  and  assume  it  even  as  an 
axiomatic  truth,  that  "  the  course  of  nature  is  uniform," 
that  u  natural  events  are  governed  by  constant  general 
laws,"  that  "  what  has  been  will  be,"  and  that  "  what  has 
been  even  in  one  instance  has  been  in  all  other  instances." 
These  are  only  different  modes  of  expressing  one  and  the 
same  Universal  Truth,  —  one  invincible  conviction  of  the 
human  mind.  This  Truth  is  the  ultimate  Major  Premise, 
upon  which  all  reasoning  from  Induction  depends,  or  which 
is  taken  for  granted  in  all  such  reasoning.  The  simplest 
and  most  indisputable  case  of  such  reasoning  depends  upon 
this  Maxim,  just  as  much  as  the  latest  and  broadest  general 
conclusion  that  has  been  propounded  in  physical  science, 
though  this  conclusion  may  be  so  questionable  that  it  is 
propounded  only  as  an  hypothesis.  I  could  not  be  sure,  for 
instance,  that  the  identical  piece  of  coin  now  in  my  hand 
still  possesses  the  same  weight,  malleability,  hardness,  pu- 
rity, &c,  which  I  ascertained  from  actual  observation  that 
it  had  only  five  minutes  ago,  if  it  were  not  for  this  irresisti- 
ble belief  in  the  uniformity  of  nature's  laws.  Whatever 
doubts  may  perplex  or  weaken  the  inference  from  some  to 
all,  these  doubts  do  not  concern  the  Primary  Truth  upon 


INDUCTION  AND  ANALOGY.  389 

which  all  such  inferences  are  based,  but  relate  solely  to  the 
correctness  of  the  Classification  over  which  the  inference 
extends.  Is  it  certain  that  we  have  classified  rightly  ? 
that  the  cases  brought  together  are  really  parallel  in  all 
essential  respects  ?  If  so,  one  instance  is  just  as  good  to 
base  an  Induction  upon  as  ten  thousand ;  for  we  have  an 
irresistible  conviction  that,  as  the  law  thus  operates  in  one 
case,  it  must  so  operate  in  all.  What  is  the  ground  of  our 
assumption  of  this  General  Truth  ?  How  came  we  to  be 
convinced  thus  absolutely  that  nature's  course  is  uniform  ? 
He  who  can  answer  this  question  has  solved  the  great 
problem  in  the  philosophy  of  Induction. 

Dr.  Reid,  Mr.  Stewart,  and  most  of  the  other  Scotch 
philosophers,  attempt  to  resolve  our  assumption  of  this 
Maxim  into  an  ultimate  fact,  into  an  original  and  instinc- 
tive law  of  the  human  mind.  Experience  is  constantly 
tending  to  confirm  it,  but  they  hold  that  we  believe  in  it 
previously  to  all  experience.  They  do  not  identify  it  with 
the  principle  of  Causation,  —  with  the  law  that  every  event 
must  have  a  Cause,  —  but  maintain  that  it  is  a  distinct  and 
independent  Axiom.  Dr.  Brown  even  goes  so  fir  as  to  at- 
tempt to  resolve  the  law  of  Causality  itself  into  this  Axiom. 
He  asserts  that  we  are  ob  jged  to  refer  every  event,  every 
beginning  to  be,  to  some  Cause,  because  we  have  an  instinc- 
tive anticipation  of  the  uniformity  of  nature's  laws.  My 
own  opinion,  as  will  be  seen  hereafter,  is  exactly  the  re- 
verse of  Brown's  theory.  It  seems  to  me  that  our  irre- 
sistible conviction  of  the  truth  of  this  Maxim,  that  nature's 
course  is  uniform,  is  resolvable  into  our  necessary  belief 
of  the  law  of  Causality;  that  the  latter  is  the  primitive 
judgment  a  priori,  and  the  former  is  secondary  and  de- 
rivative ;  that  a  process  of  Thought,  an  act  of  Reasoning, 
if  not  an  appeal  to  experience,  always  precedes,  and  is 
used  to  confirm  or  prove,  our  assertion  that  nature's  course 
is  uniform,  whfo  we  affirm  at  once,  antecedently  to  all  ex- 


390  INDUCTION  AND  ANALOGY. 

perience,  and  without  any  attempt  at  proof,   that  every 
event  must  have  a  Cause. 

But  however  this  may  be,  the  doctrine  in  which  Brown 
agrees  with  Reid  and  Stewart,  that  we  have  an  instinctive 
and  a  priori  conviction  that  nature's  laws  are  unchange- 
able, appears  plainly  indefensible.  Entia  non  sunt  mul- 
tiplicanda  prceter  necessitatem ;  it  is  a  cardinal  maxim  in 
philosophy,  that  no  principle  can  be  admitted  as  an  ulti- 
mate fact  until  it  is  clearly  shown  that  it  cannot  be  ex 
plained  as  derivative.  Indirectly,  therefore,  this  doctrim 
is  refuted  by  the  proof,  which  will  subsequently  be  at> 
tempted,  that  this  principle  is  resolvable  into  the  law  oi 
Causality.  But  still  further :  —  any  conviction,  which  is  a 
priori  in  its  origin  and  character,  must  be  universal,  neces- 
sary, and  immediate.  Now  without  going  so  far  as  Comte 
and  Mill,  who  maintain,  with  respect  to  this  principle,  thai 
"  far  from  being  the  first  Induction  we  make,  it  is  one  of 
the  last,"  that  "it  was  only  acquired  gradually,  and  ex- 
tended itself,  as  observation  advanced,  from  one  order  of 
phenomena  to  another,"  and  that  "there  are  cases,  in 
which  we  reckon  with  the  most  unfailing  confidence  upon 
uniformity,  and  other  cases  in  which  we  do  not  count  upon 
it  at  all";  —  without  adopting  these  assertions,  I  say,  it 
may  safely  be  pronounced,  that  we  do  not  accept  this  prin- 
ciple at  first,  or  in  all  cases,  unless  it  is  justified  by  some 
reflection  or  experience  ;  that  is,  until  we  have  satisfied 
ourselves  that  it  is  a  necessary  consequence  of  some  intui- 
tive and  imperative  belief,  or  have  verified  it  by  subsequent 
observations.  Through  the  law  of  the  Association  of  Ideas, 
it  is  true,  the  recurrence  of  any  phenomenon  suggests  all 
the  circumstances  by  which  it  was  originally  accompanied ; 
it  may  even  incline  us  to  believe  that  these  circumstances, 
also,  will  recur  in  the  same  order  as  before.  Even  the  dog 
cowers  at  the  sight  of  the  whip  which  has  once  or  twice 
been  used  to  punish  him.     But  this  is  very  far  from  an 


INDUCTION  AND  ANALOGY.  391 

immediate  and  necessary  conviction  that  any  of  these  for- 
mer concomitants  must  so  recur.  We  stop  to  analyze  the 
case  and  make  distinctions ;  we  separate  the  conjunctions 
that  are  believed  to  be  invariable  from  those  that  are 
merely  casual,  and  accept  the  former  only  because  we 
recognize  one  of  the  events  either  as  a  Cause,  or  what  is 
believed  to  be  the  regular  concomitant  of  a  Cause,  of  the 
other. 

"  Every  person's  consciousness,"  says  Mr.  Mill,  "assures 
him  that  he  does  not  always  expect  uniformity  in  the  course 
of  events ;  he  does  not  always  believe  that  the  unknown 
will  be  similar  to  the  known,  that  the  future  will  resemble 
the  past.  Nobody  believes  that  the  succession  of  rain  and 
fine  weather  will  be  the  same  in  every  future  year  as  in 
the  present.  Nobody  expects  to  have  the  same  dreams 
repeated  every  night.  On  the  contrary,  everybody  men- 
tions it  as  something  extraordinary,  if  the  course  of  nature 
is  constant,  and  resembles  itself,  in  these  particulars.  To 
look  for  constancy  where  constancy  is  not  to  be  expected, 
as,  for  instance,  that  a  day  which  has  once  brought  good 
fortune  will  always  be  a  fortunate  day,  is  justly  accounted 
superstition.  The  course  of  nature,  in  truth,  is  not  only 
uniform,  it  is  also  infinitely  capricious.  Some  phenomena 
are  always  seen  to  recur  in  the  very  same  combinations  in 
which  we  met  with  them  at  first ;  others  seem  altogether 
capricious." 

On  the  other  hand,  the  doctrine  of  Comte  and  Mill,  that 
our  conviction  of  the  uniformity  of  nature's  laws,  which  is 
the  ground  or  principle  upon  which  all  Induction  rests,  is 
itself  obtained  by  Induction,  appears  to  be  an  evident  beg- 
ging of  the  question.  How  can  any  mental  operation  be 
used  as  a  means  of  discovering  and  verifying  a  principle 
which  must  be  taken  for  granted  before  that  operation  it- 
self can  be  performed  ?  To  obtain  a  number  of  Conclusions 
by  adopting  a  certain  Maxim  as  a  Major  Premise,  and  then 


392  INDUCTION   AND   ANALOGY. 

to  use  those  very  Conclusions  as  a  means  of  proving  that 
Maxim,  is  evidently  reasoning  in  a  circle.  Mr.  Mill  is  per- 
fectly aware  of  this  objection  to  his  doctrine,  and  frankly 
states  it  in  the  strongest  terms.  "  Can  we  prove  a  prop- 
osition," he  asks,  "  by  an  argument  which  takes  it  for 
granted  ?  And  if  not  so  proved,  on  what  evidence  does  it 
rest?" 

But  though  aware  of  the  objection,  it  does  not  appear 
that  Mr.  Mill  has  been  successful  in  his  endeavors  to  ob- 
viate it.  He  rather  augments  the  difficulty,  by  admitting 
that  the  Maxim  "  was  not,  of  course,  derived  from  rigid 
Induction,  but  from  the  loose  and  uncertain  mode  of  Induc- 
tion per  enumerationem  simplicem."  Then  the  Premise 
rests  upon  less  satisfactory  evidence  than  the  Conclusion, 
and  yet  the  latter  is  based  exclusively  upon  the  former. 
Is  not  this  a  contradiction  ?  How  can  the  superstructure 
be  more  stable  than  the  very  foundation  on  which  it  rests  ? 

Induction  by  simple  enumeration  "  consists  in  ascribing 
the  character  of  general  truths  to  all  propositions  which  are 
true  in  every  instance  that  we  happen  to  know  of."  Thus, 
we  say  that  "All  ruminating  animals  divide  the  hoof," 
merely  because  no  instance  to  the  contrary  has,  as  yety 
been  discovered.  But  "  to  Europeans,  not  many  years 
ago,  the  proposition,  'All  swans  are  white,'  appeared  an 
equally  unequivocal  instance  of  uniformity  in  the  course 
of  nature.  Further  experience  has  proved  that  they  were 
mistaken."  Then  the  presumption  in  favor  of  what  is  still 
the  accepted  rule,  in  the  present  state  of  our  knowledge, 
that  all  ruminating  animals  divide  the  hoof,  would  not  be 
held  to  outweigh  the  testimony  of  one  unimpeachable  wit- 
ness, who  should  declare  that,  in  some  hitherto  imperfectly 
explored  region,  he  had  discovered  a  solid-hoofed  ruminat- 
ing animal.  How  can  the  evidence  of  these  merely  pro- 
visional truths,  which  are  liable  to  be  overturned  at  any 
moment,  be  the  same  with  that  which  supports  the  validity 


INDUCTION  AND  ANALOGY.  393 

ti  the  Maxim  upon  which  the  most  rigorous  Inductions  de- 
pend ? 

Mr.  Mill  answers,  that  even  this  precarious  Induction, 
that  something  is  universally  true  because  we  have  never 
known  any  instance  to  the  contrary,  may  become  a  valid 
ground  of  belief  when  it  is  preceded  by  the  assurance,  that, 
"  if  there  were  in  nature  any  instances  to  the  contrary,  we 
should  have  known  of  them."  An  empirical  law,  he  argues, 
"  of  which  the  truth  is  exemplified  at  every  moment  of 
time,  and  in  every  variety  of  place  or  circumstance,  has  an 
evidence  which  surpasses  that  of  tlie  most  rigid  Induction, 
even  if  the  foundation  of  scientific  Induction  were  not  itself 
laid,  as  we  have  seen  that  it  is,  in  a  generalization  of  this 
very  description."  As  to  the  admissions  made  in  the  pas- 
sage which  has  just  been  quoted  from  Mr.  Mill,  that  we  do 
"  not  always  expect  uniformity  in  the  course  of  events," 
and  that  "  the  course  of  nature,  in  truth,  is  not  only  uni- 
form, it  is  also  infinitely  capricious,"  it  is  claimed  that  the 
progress  of  Inductive  Science  has  already  explained  away 
these  apparent  exceptions.  This  progress  has  been  so 
great,  it  is  argued,  that  we  now  know  directly  that  the 
Maxim  holds  good  of  far  the  greater  number  of  phenom- 
ena, "  the  utmost  that  can  be  said  being  that  of  some  we 
cannot  positively,  from  direct  evidence,  affirm  its  truth  ; 
while  phenomenon  after  phenomenon,  as  they  become  bet- 
ter known  to  us,  is  constantly  passing  from  the  latter  class 
into  the  former ;  and  in  all  cases  in  which  that  transition 
has  not  yet  taken  place,  the  absence  of  direct  proof  is  ac- 
counted for  by  the  rarity  or  the  obscurity  of  the  phenomena, 
or  our  deficient  means  of  observing  them,  or  the  logical  dif- 
ficulties arising  from  the  complication  of  the  circumstances 
in  which  they  occur." 

But  even  when  the  doctrine  is  thus  limited  and  ex- 
plained, it  does  not  appear  to  be  relieved  from  the  two  fun- 
damental objections  which  have  been  urged  against  it,  first, 
17* 


394  INDUCTION   AND  ANALOGY. 

that  it  founds  the  principle  of  Induction  upon  Induction 
itself,  which  is  reasoning  in  a  circle,  and  secondly,  that  it 
bases  a  stronger  conviction  upon  a  weaker  one,  a  higher 
probability  upon  a  lower  one.  Granted,  if  you  will,  that 
Induction  itself,  a  rude  Induction,  gradually  leads  us  to  be- 
lieve in  rigorous  scientific  Induction  ;  this  may  explain  the 
genesis  of  the  phenomenon,  or  how  it  was  that  we  were 
first  led  to  employ  this  organon  of  discovery.  But  before 
we  can  accept  the  fruit  of  the  Induction  with  the  strong 
and  unhesitating  conviction  which  we  now  accord  to  any 
well-established  Law  of  Nature,  we  must  not  only  know 
how  we  were  first  induced  to  believe  that  such  a  Law 
exists,  but  we  must  find  some  valid  principle  which  may 
fairly  be  accounted  a  proof  of  its  existence.  Certainly  such 
proof  cannot  be  obtained  by  reasoning  in  a  circle.  Mill 
and  Comte  would  have  us  believe,  that  our  invincible  con- 
viction of  the  universality  of  the  Law  of  Gravitation  rests 
upon  no  firmer  basis  than  the  opinion,  which,  indeed,  is 
daily  gaining  ground,  and  which  the  progress  of  mere  Phys- 
ical Science  evidently  tends  to  confirm,  that  everything  in 
nature  is  subject  to  law,  so  that  it  takes  place  by  a  phys- 
ical necessity,  and  might  be  predicted  with  unerring  con- 
fidence, if  we  had  a  perfect  knowledge  of  its  antecedents. 
"  Every  event  has  some  invariable  and  unconditional  ante- 
cedent "  ;  —  if  we  hesitate  to  admit  this  proposition  in  all  its 
generality,  Mr.  Mill  thinks  we  cannot  consistently  believe 
that  all  matter  gravitates,  that  oxygen  is  necessary  for  the 
support  of  animal  life,  or  even  that  fire  will  burn  and  water 
drown.  We  maintain  that  the  latter  propositions  are  in- 
contestable, while  the  former,  the  principle  of  the  univer- 
sality of  law,  is  merely  a  hypothetical  conclusion,  though 
an  extremely  probable  one.  Accordingly,  to  base  the  lat- 
ter upon  the  former  is  to  make  the  superstructure  stronger 
than  its  own  foundation.  Mr.  Mill  himself  is  compelled  to 
admit,  with  respect  to  one  very  large  class  of  phenomena, 


INDUCTION  AND  ANALOGY.  395 

those  of  the  human  will,  that  at  least  one  half  of  the  specu- 
lative world,  even  in  our  own  day,  do  not  believe  in  the 
universality  of  law,  or  that  every  event  is  necessarily  de- 
termined by  its  antecedents.  And  with  regard  even  to 
physical  events,  a  large  and  increasing  number  of  philos- 
ophers, among  whom  are  ranked  Bishop  Berkeley,  Dr. 
Samuel  Clarke,  and  Dugald  Stewart,  hold  that  none  of 
them  are  subject  to  law,  in  the  sense  of  being  absolutely 
determined  by  their  physical  antecedents,  but  are  the  re- 
sults of  volition,  which  is  free  to  modify  them  at  any  mo- 
ment. But  without  adopting  this  theory,  he  is  a  bold 
advocate  of  the  perfectibility  of  Physical  Science  who  will 
maintain  that  the  probability  of  ultimately  discovering  that 
phenomena  still  so  apparently  irregular  and  inconstant  as 
those  of  the  weather,  of  health  and  disease,  the  countless 
peculiarities  of  individual  plants  and  animals,  and  the 
equally  numerous  idiosyncrasies  of  human  intellect  and 
character,  are  subject  to  fixed  and  definite  laws,  is  so  great, 
that  we  may  safely  rest  upon  it  all  our  confidence  in  the 
physical  laws  that  have  already  been  established ;  —  that 
this  probability  is  the  measure  and  the  test  of  all  the  cer- 
tainty that  has  hitherto  been  obtained  in  Physical  Science. 

Let  us  examine,  then,  the  only  remaining  theory,  which 
is,  that  the  ultimate  Ground  of  Induction  is  the  Law  of 
Causality,  or  the  judgment  that  every  event  must  have  a 
Cause,  —  not  merely  a  constant  physical  antecedent,  but  an 
efficient  Cause.  It  is  only  necessary  to  show,  that  the  Law 
of  Causality  is  readily  and  naturally  explicated  into  the 
Maxim  that  nature's  course  is  uniform,  so  that  the  abso- 
lute and  imperative  conviction,  which  belongs  to  the  for- 
mer as  an  a  priori  cognition  of  the  human  mind,  is  trans- 
ferred, by  an  easy  association  of  ideas,  to  the  latter,  though 
not  logically  belonging  to  it. 

Take  the  simplest  case  of  Induction,  by  which  we  are 
led  to  expect  that  any  physical  object  will  always  continue 


396  INDUCTION   AND  ANALOGY. 

to  manifest  the  same  qualities  that  have  hitherto  been  ob- 
served in  it,  unless  it  is  exposed  to  some  new  influences,  or 
a  new  antecedent  is  brought  in.  Here  the  assumption  evi- 
dently is,  that  the  qualities  of  the  same  thing  are  perma- 
nent, unless  some  Cause  intervenes  to  change  them ;  and 
this  assumption  is  logically  certain,  for  it  is  an  Immediate 
Inference  from  the  Law  of  Causality,  that  no  change  what- 
ever can  take  place  in  anything  without  a  Cause.  The 
coin  must  retain  the  same  attributes  which  it  was  recently 
observed  to  possess,  if  there  has  not  been  some  Cause  of  al- 
teration. This  proviso  is  the  source  of  doubt  which  must 
always  arise  when  an  unquestionable  abstract  truth  is  ap- 
plied to  real  objects  or  actual  events.  We  never  can  be 
sure  that  such  a  Cause  of  change  has  not  intervened ;  but 
we  are  morally  certain  that  it  has  not,  if  there  has  been  no 
apparent  alteration  of  the  circumstances  of  the  case,  no 
seeming  exposure  to  new  influences.  To  this  extent,  then, 
we  can  safely  reason  from  the  past  to  the  future,  or  from 
some  to  all,  when  satisfied  that  the  Classification  is  correct, 
—  that  is,  that  no  new  occurrence  or  Efficient  Cause  has 
destroyed  the  resemblance  of  the  observed  instances  to  the 
expected  ones,  or  of  some  to  the  others. 

The  next  sort  of  Induction,  though  a  little  more  compli- 
cated, is  easily  resolved  into  the  same  Law  of  Causality.  It 
has  already  been  shown  that  among  the  other  properties 
of  any  particular  substance  must  be  ranked  its  active  and 
passive  powers,  that  is,  the  changes  in  other  bodies  of 
which  its  proximity  has  been  a  constant  antecedent,  or  the 
changes  to  which  it  is  itself  subject  when  brought  into  re- 
lation with  other  substances  under  different  circumstances. 
These  active  and  passive  powers,  regarded  as  mere  se- 
quences of  phenomena,  may  properly  be  reduced  to  the 
preceding  head  of  qualities;  they  form,  as  we  have  seen, 
one  class  of  the  attributes  of  every  substance,  and,  as  such, 
enter  into  the  Intension  of  the  Concept  which  denotes  that 


INDUCTION   AND   ANALOGY.  397 

jubstance.  In  truth,  what  are  called  secondary  qualities 
are  only  the  powers  which  bodies  possess  to  excite  certain 
sensations  in  us,  when  brought  into  relation  with  our  or- 
gans of  sense.  And  in  like  manner,  the  capacity  of  gold 
to  be  melted  on  the  application  of  a  sufficient  degree  of 
heat  is  an  integral  part  of  our  complex  notion  of  this  sub- 
stance. Powers  being  nothing  but  qualities,  then,  the  Law 
of  Causality  is  applicable  just  as  in  the  former  case  ;  these 
powers  must  be  fixed  or  constant  in  their  operation,  if  a 
new  Cause  has  not  supervened  to  alter  them.  The  general 
maxim  is  one  of  absolute  certainty,  but  in  its  application  to 
a  given  case  we  never  can  be  sure  that  the  proviso  in  it 
has  been  rigidly  fulfilled.  This  doubt  must  always  remain, 
and  is  usually  more  serious,  and  less  capable  of  being  re- 
duced by  further  observation  and  experiment,  as  regards 
the  powers,  than  with  respect  to  the  other  qualities,  of  bod- 
ies. The  circumstances  to  be  observed  in  order  to  prevent 
the  intrusion  of  a  new  antecedent  are  more  numerous  and 
complex ;  we  cannot  so  easily  be  assured  that  the  cases  are 
strictly  parallel.  The  unexpected  presence  of  a  little  more 
or  less  carbon  may  have  diminished  the  fusibility  of  the 
metal ;  if  a  large  mass  of  iron  be  near,  the  action  of  the 
magnetic  needle  is  disturbed. 

Still  further  ;  —  it  is  now  known  that  the  merely  physi- 
cal antecedents  and  other  circumstances  are  not  the  Effi- 
cient Cause  of  the  phenomenon,  but  are  believed  to  be  its 
regular  concomitants  only  because  their  presence,  thus  far, 
has  been  invariably  followed  by  the  effect.  Accordingly, 
whatever  assurance  we  may  possess  that  the  outward  cir- 
cumstances are  unchanged,  it  is  still  possible  that  the  real 
Cause  may  be  so  far  modified  that  the  expected  result  will 
no  longer  be  produced.  The  doubt  which  thus  rests  upon 
the  case  cannot  be  dispelled  by  any  precautions  whatsoever. 
The  cases  may  be  strictly  parallel  in  every  visible  respect, 
as  tested  by  the  nicest  observations  ;  but  if  the  physical 


398  INDUCTION   AND   ANALOGY. 

antecedent  was  only  the  occasion,  and  not  the  Cause,  the 
phenomenon  may  not  be  repeated,  as  it  is  always  possible 
that  the  true  Cause  may  now  for  the  first  time  exist  under 
different  combinations.  To  recur  to  the  illustration  taken 
from  Mr.  Babbage's  machine ;  —  though,  in  countless  in- 
stances, each  number  presented  has  been  greater  than  its 
immediate  predecessor  by  unity,  yet  as  this  constant  pre- 
cursor was  not  the  true  Cause  which  determined  the  num- 
ber that  was  to  come  after  it,  it  is  always  conceivable  that 
the  next  presentation  should  be  of  an  entirely  novel  char 
acter. 

We  can  now  see  why  it  is  that  the  Maxim  which  is  the 
Ground  of  Induction,  and  on  the  assumption  of  which  the 
validity  of  all  our  reasoning  about  real  objects  and  actual 
events  depends,  appears  so  unquestionably  true  that  we 
regard  it  as  an  Axiom.  To  say  that  nature's  course  is 
uniform,  and  that  all  events  are  subject  to  law,  is  only  to 
assert  our  intuitive  conviction,  that  every  phenomenon  must 
have  an  Efficient  Cause,  that,  while  the  Cause  remains 
the  same,  the  effect  must  be  constant  and  proportional  to  it, 
and  hence,  that,  whenever  the  true  Cause  is  discovered,  we 
are  enabled  to  predict  unerringly  the  recurrence  of  the 
effect.  The  relation  between  a  true  Cause  —  that  is,  an 
efficient  Cause  —  and  its  effect,  is  radically  unlike  that  be- 
tween a  physical  antecedent  and  its  physical  consequent. 
No  absolute  conviction,  no  law  of  the  human  mind,  mani- 
festing itself  anterior  to  all  experience,  and  thereby  first 
rendering  experience  possible,  asserts  any  connection  be- 
tween antecedent  and  consequent  like  that  which  exists 
between  Cause  and  effect.  The  relation  between  the  two 
former,  that  of  mere  succession  in  time,  is  contingent,  rest- 
ing solely  upon  experience,  and  liable  to  be  overturned  at 
any  moment  by  subsequent  experience ;  between  the  two 
latter,  it  is  a  Causal  relation,  and,  as  such,  is  absolute  and 
unchangeable,  for  it  is  irreversible  even  in  thought.     What 


INDUCTION  AND  ANALOGY.  399 

de  we  mean  when,  as  a  ground  of  reasoning  from  some  to 
all,  we  assert  that  nature  acts  uniformly,  or  that  all  phys- 
ical events  are  subject  to  law  ?  Not,  surely,  that  a  given 
antecedent  must  always  be  followed  by  that  particular  phe- 
nomenon which,  according  to  all  experience  thus  far,  has 
been  its  invariable  consequent.  This  is  the  only  conclu- 
sion which  mere  Induction  aims  to  establish ;  but  it  is  not 
competent  to  serve  as  the  Ground  of  Induction  itself,  or  as 
that  Premise  which  must  be  taken  for  granted  before  rea- 
soning by  Induction  is  possible.  But  we  mean  only  that 
the  sequence  in  question  is  necessary,  if  the  antecedent  is 
the  Efficient  Cause  (or  the  invariable  concomitant^  sign,  or 
precursor  of  such  Cause)  of  the  consequent.  We  mean 
only  to  assert  the  existence  of  an  irreversible  law,  and  not 
necessarily  that  such  law  has  already  been  discovered. 
Comte  and  all  his  followers  will  tell  us  that  no  event,  how- 
ever extraordinary  and  unexpected,  is  to  be  deemed  a 
miracle,  —  that  is,  a  violation  of  law,  —  because  the  pre- 
sumption is,  that  further  research  will  either  reveal  a  new 
law,  or  an  improved  expression  of  an  old  one,  under  which 
the  occurrence,  however  strange  and  marvellous,  may  nat- 
urally be  subsumed.  He  will  say,  —  to  adopt  a  well-worn 
illustration,  —  that  the  conversion  of  water  into  a  solid  was 
a  miracle  to  the  King  of  Siam ;  but  with  our  larger  expe- 
rience, it  is  no  miracle  to  us,  for  we  have  even  discovered 
the  law,  —  that  is,  the  constant  antecedent,  —  under  which 
the  formation  of  ice  takes  place.  What  is  this  but  to  assert 
that  our  conviction  of  the  universality  and  permanence  of 
law,  so  far  from  being  derived  from  experience,  so  far  from 
resting  on  that  very  process  of  Induction  of  which  it  is  the 
sole  support,  is  strong  enough  to  contradict  all  experience, 
and  to  maintain  its  place  as  an  Axiom,  though  contradicted 
by  the  largest  and  most  cautious  Induction  which  human 
science  has  ever  framed  ?  Not  even  the  resurrection  of  a 
dead   man,   says   the   Positivist,   would  be  a  violation  of 


400  INDUCTION  AND   ANALOGY. 

law ;  — >  then  his  conviction  of  the  permanence  of  nature  s 
laws  overrides  all  the  evidence  of  experience,  and  contra- 
dicts the  whole  tenor  of  modern  Inductive  science. 

What  is  called  physical  necessity  is  nothing  but  a  convic- 
tion that  the  relation  of  an  Efficient  Cause  to  its  effect  is 
unalterable,  coupled  with  the  assumption,  which  is  a  natural 
one,  but  still  illogical,  either  that  the  particular  antecedent 
or  concomitant  phenomenon  is  itself  the  Cause,  or  is  so 
closely  connected  with  it  that  its  presence  must  always  be 
followed  by  the  recurrence  of  the  effect.  The  only  ground 
of  this  assumption  is  the  invariability  of  the  succession  in 
time,  or  the  fact  that,  so  far  as  our  experience,  or  as  all 
human  experience,  has  extended,  the  one  phenomenon  has 
always  been  the  immediate  consequent  of  the  other.  That 
this  ground  is  insufficient  to  justify  us  in  calling  the  succes- 
sion a  necessary  one  has  already  been  abundantly  proved. 
The  Positivists,  in  their  desire  to  eliminate  the  notion  of 
cause  altogether,  although  they  are  compelled  to  retain  the 
word  and  all  the  associations  connected  with  it,  refuse  to 
attribute  the  phenomenon  to  any  single  antecedent.  The 
invariable  sequence,  they  say,  exists  between  a  consequent 
and  the  sum  of  its  several  antecedents,  all  of  which  must 
concur  before  we  can  be  sure  of  the  presence  of  the  effect. 
In  other  words,  what  they  call  a  cause  is  only  an  assem- 
blage of  the  conditions,  all  of  which  must  be  fulfilled  before 
the  phenomenon  can  be  reproduced.  "  The  real  Cause," 
says  Mr.  Mill,  "  is  the  whole  of  these  antecedents  ;  and  we 
have,  philosophically  speaking,  no  right  to  give  the  name 
of  cause  to  one  of  them,  exclusively  of  the  others."  And 
again,  "  the  Cause  is  the  sum  total  of  the  Conditions,  posi- 
tive and  negative,  taken  together ;  the  whole  of  the  con- 
tingencies of  every  description,  which,  being  realized,  the 
consequent  invariably  follows."  Among  these  "  negative  " 
conditions,  or  rather,  as  the  sum  of  them,  he  ranks  "  the 
absence  of  preventing  or  counteracting  Causes."     In  con- 


INDUCTION  AND  ANALOGY.  401 

formity  with  this  view,  the  distinction  between  agent  and 
valient,  between  something  which  acts  and  some  other 
thing  which  is  acted  upon,  is  formally  abolished,  as  it  is 
denied  that  there  is  any  action  in  the  case.  An  inevitable 
corollary  of  this  doctrine  is,  that  there  is  no  power  or  effi- 
ciency in  any  one  of  the  antecedents  the  exertion  of  which 
necessarily  creates  the  effect.  Yet  the  denial  of  any  such 
causal  agency  entirely  refutes  the  hypothesis  that  there 
is  any  necessary  connection  between  the  two  events,  and 
leaves  their  union  merely  a  contingent  one,  liable  to  be 
dissolved  or  contradicted  by  subsequent  experience.  By 
rejecting  the  doctrine  of  Efficient  Causation,  the  Positivist 
theory  throws  away  all  evidence  of  the  permanence  and 
universality  of  nature's  laws. 

This  conclusion  will  appear  still  more  obvious  when  it  is 
demonstrated,  as  can  very  easily  be  done,  that  every  pro- 
cess of  Inductive  Reasoning,  however  rigidly  conducted, 
and  however  verified  by  subsequent  observations,  is  still  re- 
solvable, in  the  last  analysis,  into  the  despised  "  Induction 
by  simple  enumeration,"  which  Lord  Bacon  calls  mera  pal- 
patio, or  groping  in  the  dark.  The  best  evidence  which 
physical  science  has  been  able  to  collect  in  support  of  the 
most  generally  recognized  Laws  of  Nature  amounts  only  to 
this,  that  they  are  found  to  be  true  in  every  instance  that 
we  happen  to  know  of.  Mr.  Mill  admits  that  Induction 
necessarily  commences  with  this  very  imperfect  evidence  ; 
and  he  should  have  added,  that  it  also  proceeds  and  ends 
with  it,  finding  no  other  or  stronger  basis  on  which  to  rest 
its  conclusions. 

Nearly  all  the  additional  evidence  which  the  advance- 
ment of  science  procures  for  those  conclusions  which  were 
at  first  avowedly  accepted  as  inferences  from  Induction  by 
simple  enumeration,  (perhaps  from  an  enumeration  only  of 
a  few  instances,  or  even  from  a  single  case,)  arises  eithei 
from  extended  observation  and  experiment,  from  an  im 


402  INDUCTION  AND   ANALOGY. 

proved  classification  of  the  objects  about  which  we  reason, 
or  from  what  Dr.  Whewell  calls,  by  a  happily  invented 
phrase,  the  consilience  of  several  Inductions.  The  process 
of  Induction,  when  considered  as  an  operation  of  mind,  or 
as  a  sort  of  inference,  is  essentially  one  and  the  same,  and 
perfectly  determinate  in  character.  There  are  not  several 
kitids  of  it,  though  there  are  various  degrees  of  caution, 
precision,  and  thoroughness  with  which  it  is  carried  out. 
It  is  always  employed  with  reference  to  a  class  of  objects, 
qualities,  or  events,  whether  that  class  be  well  or  ill  formed, 
that  is,  whether  the  members  of  it  do,  or  do  not,  agree 
with  each  other  in  all  material  respects  ;  and  it  always  pro- 
ceeds from  some  to  all  of  that  class,  whether  the  conclusion 
thus  formed  does,  or  does  not,  coincide  or  harmonize  with 
other  conclusions  obtained  by  a  perfectly  similar  process, 
though  from  other  data,  and  with  a  different  purpose  in 
view.  The  village  matron,  undertaking  to  prescribe  for 
the  illness  of  her  neighbor's  child  from  what  she  judges  to 
be  the  similar  cases  that  have  happened  in  her  own  family, 
and  Sir  Humphry  Davy,  anticipating  that  his  mode  of 
analyzing  potash  into  the  oxide  of  a  new  metal  would  not 
only  hold  good  of  all  other  lumps  of  potash  besides  the 
very  one  he  was  experimenting  upon,  but  would  be  found 
practicable,  and  would  lead  to  similar  results,  in  the  case 
of  other  alkalis  and  earths,  are  both  alike  reasoning  from 
Induction  by  simple  enumeration.  The  only  difference  is, 
that  the  diseases  which  affect  the  human  frame  are  very 
numerous,  and,  as  they  have  but  few  recognizable  symp- 
toms, can  be  but  imperfectly  classified  at  best,  and  a  village 
matron  would  probably  classify  them  very  ill,  so  that  her 
inference  from  some  to  all  would  be  wrong ;  while  the 
alkalis  are  few  in  number,  and  have  determinable  and 
strongly  marked  common  qualities,  so  that  the  correspond- 
ing inference  in  their  case  was  entirely  safe. 

Attempts  have  been  made  at  various  times  to  frame  what 


INDUCTION  AND   ANALOGY.  403 

• 
may  be  called  a  "  Logic  of  Induction,"  or  a  full  analysis 
and  description  of  the  operations  by  which  we  proceed  to 
the  discovery  of  physical  laws.  Lord  Bacon,  who  made 
the  earliest  and  most  remarkable  endeavor  of  this  sort, 
hoped  to  furnish  a  method  of  scientific  investigation  which 
should  be  so  complete  and  accurate  as  to  constitute  an  or- 
ganon  of  discovery,  and  reduce  all  intellects  to  a  level, 
making  success  in  the  search  after  truth  a  matter  merely 
of  time  and  labor.  Taught  by  experience  that  discoveries 
cannot  be  thus  made  by  rule,  but  are  generally  the  results 
of  a  tentative  process  many  times  repeated,  and  a  happy 
combination  of  circumstances,  the  later  followers  of  Lord 
Bacon  have  attempted  merely  to  analyze  and  describe  the 
process  by  which  discoveries  have  been  made,  without  hop- 
ing to  indicate  any  sure  method  of  adding  to  their  number. 
But  even  this  endeavor,  though  aided  by  all  the  lights  of 
modern  physical  science,  and  prosecuted  by  such  eminent 
thinkers  as  Sir  John  Herschel,  Dr.  Whewell,  and  Mr.  J. 
S.  Mill,  has  had  but  very  limited  success.  The  results  do 
not  agree ;  though  the  same  compound  phenomena  are  pre- 
sented for  examination,  they  are  analyzed  by  these  three  in- 
quirers into  very  different  elements  and  processes  of  thought. 
These  theorists  do  not  even  hold  the  same  opinion  as  to 
the  nature  of  the  process  which  they  have  to  separate  into 
its  elements,  or,  in  other  words,  as  to  what  constitutes  In- 
duction. Dr.  Whewell,  fearful  of  resting  the  whole  cer- 
tainty of  physical  science  upon  so  narrow  and  unstable  a 
basis  as  reasoning  in  respect  merely  to  all  the  cases  that  we 
happen  to  know  of,  boldly  restricts  the  name  of  Induction 
to  what  seems  to  be  a  mere  generalization  of  the  facts 
already  observed,  but  as  now  seen  under  a  new  light  be- 
cause succinctly  comprehended  in  one  general  formula; 
and  appears  to  lose  sight  altogether  of  the  necessity,  if 
science  is  to  fulfil  its  office  of  anticipation  and  prediction, 
of  extending  the  generalization  to  all  the  objects  and  events 


404  INDUCTION  AND  ANALOGY. 

of  a  given  class,  whether  they  have  yet  been  observed  or 
not.  Mr.  J.  S.  Mill,  who  has  more  confidence  in  the  pre- 
cautions and  the  means  of  verification  by  which  men  of 
science  test  and  confirm  the  rude  Inductions  of  the  vulgar, 
justly  assents  that  Dr.  Whe well's  mere  "  Colligation  of 
Facts,"  far  from  being  the  type  of  Induction  generally, 
"is  not  Induction  at  ail,"  but  only  a  new  description  of 
the  phenomena.  He  undertakes  to  analyze  and  reduce  to 
system  these  precautions  and  means  of  subsequent  verifi- 
cation, and  to  show  that,  when  they  are  duly  observed 
and  practised,  scientific  Induction  differs  in  kind,  and  not 
merely  in  degree,  from  Induction  by  simple  enumeration, 
and,  though  based  merely  on  experience,  establishes  its 
conclusions  with  the  highest  certainty  of  which  the  human 
mind  is  capable.  But  experience,  from  its  very  nature, 
cannot  extend  beyond  a  limited  number  of  cases ;  and  as 
even  the  most  cautious  and  rigorous  Induction  avowedly 
has  no  other  foundation  than  experience,  either  the  abso- 
lute universality  of  the  Laws  of  Nature  is  not  scientifically 
established,  or  it  must  be  deduced  from  a  priori  considera- 
tions respecting  the  relation  of  an  Efficient  Cause  to  its 
effects.  The  consilience  of  several  Inductions  merely  ex- 
tends the  enumeration  to  a  larger  number  of  cases ;  but 
any  such  extension,  of  course,  cannot  include  future  in- 
stances, nor  in  any  way  enlarge  the  domain  of  possible  ex- 
perience. In  fact,  most  of  the  scientific  processes,  which 
are  ably  analyzed  by  Mr.  Mill,  have  reference  to  the  use  of 
Induction  as  an  organon  of  discovery,  and  not  as  a  medium 
of  proof;  they  point  out  the  inferences  which  we  ought  to 
make,  but  they  do  not  render  any  more  stable  the  founda- 
tion by  which  all  such  inferences  are  supported.  And  any 
improvements  in  the  modes  of  observation,  or  in  the  classi- 
fication of  the  things  observed,  are  merely  preparatory  to 
the  process  of  Induction,  and  do  not  in  any  way  affect  the 
essential  nature  of  that  process. 


INDUCTION  AND   ANALOGY.  405 

Putting  aside  the  terminology  invented  by  Dr.  Whewell, 
and  also  that  recommended  by  Mr.  Mill,  as  not  even  their 
authority  has  sufficed  to  bring  either  into  common  use,  it 
may  be  said  that  there  are  but  three  phrases  generally  em- 
ployed to  designate  those  results  of  Induction  which  con- 
stitute the  highest  generalizations  of  science.  These  are 
a  General  Fact,  a  Law  of  Nature,  and  a  Cause,  this  last 
being  now  usually  understood  to  mean  nothing  more  than 
an  Invariable  Antecedent.  Unfortunately,  even  these  three 
phrases  are  so  wavering  and  uncertain  in  their  significa- 
tion, that  they  are  often  employed  as  synonymes,  while 
hardly  any  scientific  person  is  consistent  in  the  use  which 
he  makes  of  them,  and  no  two  writers  upon  the  philosophy 
of  the  physical  sciences  agree  with  each  other  in  the  at- 
tempt to  limit  and  define  their  meaning. 

The  first  of  the  number,  a  General  Fact,  though  em- 
ployed with  somewhat  more  precision  and  consistency  than 
the  other  two,  is  yet  of  narrow  and  indeterminate  range, 
and  is  grudgingly  used,  because  it  is  modest  in  pretension, 
and  does  not  feed  the  pride  of  science,  or  gratify  the  van- 
ity of  the  inquirer  into  the  secrets  of  nature.  It  coincides 
with  what  Mr.  Mill  calls  an  Empirical  Law,  or  the  result 
of  an  Induction  by  simple  enumeration.  Thus,  it  is  prop- 
erly a  General  Fact  that  all  horned  animals  are  ruminant, 
that  all  quadrupeds  are  viviparous,  that  every  living  thing 
is  produced  from  an  egg,  that  opium  and  alcohol  intoxicate, 
&c.  But  the  phrase  is  sparingly  used,  because  we  are  not 
content  simply  to  point  out  a  new  characteristic  of  a  whole 
class  of  objects,  or  to  form  a  new  class  of  facts  by  tracing 
their  hitherto  unsuspected  agreement  with  each  other,  so 
far  as  our  observation  has  extended,  in  some  latent  attri- 
bute. We  aspire  to  the  much  higher  praise  of  determin- 
ing a  new  "  Law  of  Nature,"  which  must  hold  true  on  all 
occasions,  whether  observed  or  not,  and  the  discovery  of 
which  is  therefore  equivalent  to  a  revelation  of  another  of 


406  INDUCTION   AND   ANALOGY. 

the  immutable  purposes  of  the '  Almighty.  The  General 
Fact  is  admitted  to  be  true  only  so  far  as  our  observation 
has  extended,  or  at  any  rate  to  afford  comparatively  but  a 
slight  presumption  that  it  will  be  found  to  hold  good  in 
cases  as  yet  unobserved.  But  as  already  remarked,  the 
narrower  and  the  more  definite  the  class,  the  stronger  is 
this  presumption.  Thus,  that  every  antelope  is  ruminant, 
is  a  far  more  probable  conclusion  than  that  all  horned  ani- 
mals are  ruminant;  we  admit  very  readily  that  all  the 
mammalia  are  produced  from  eggs,  but  not  so  readily  that 
the  whole  animal  kingdom  are  thus  produced. 

A  Law  of  Nature,  in  its  more  definite  signification,  is 
employed  to  designate  a  group  or  series  of  General  Facts, 
relating  to  the  same  subject  or  class  of  subjects,  and  differ- 
ing from  each  other  by  some  mode  of  proportional  varia- 
tion, so  that  the  place  of  every  member  of  the  series  may 
be  easily  deduced  from  one  numerical  formula.  Such  are 
Kepler's  laws  of  the  planetary  motions,  the  law  of  definite, 
reciprocal,  and  multiple  proportions  in  Chemistry,  and  of 
phyllotaxis  in  Botany.  The  General  Facts  may  be  known, 
long  before  their  relation  to  each  other,  or  their  law  of 
proportional  variation,  is  discovered.  Thus,  the  General 
Fact  that  the  leaves  of  the  apple-tree  are  disposed  in  cycles 
of  fives,  and  so  that  the  spiral  line  connecting  their  points 
of  insertion  passes  twice  round  the  stem  for  each  cycle, 
their  arrangement  being  thus  conveniently  denoted  by  the 
fraction  |,  was  ascertained,  and  a  corresponding  General 
Fact  for  many  other  species  of  plants  was  equally  well 
known,  before  the  "  Law  "  was  discovered,  that  the  result- 
ing fractions  fall  into  a  series,  any  one  of  which  has  for  its 
numerator  the  sum  of  the  two  preceding  numerators,  and 
for  its  denominator  the  sum  of  the  two  preceding  denomi- 
nators. So,  also,  the  General  Facts  in  Optics,  that  the 
angle  of  refraction,  measured  from  the  perpendicular  to 
the  surface  of  any  medium  heavier  than  air,  is  always  less 


INDUCTION  AND  ANALOGY.  407 

than  the  angle  of  incidence,  and  is  not  proportional  to  it, 
were  commonly  known,  and  even  Tables  had  been  labori- 
ously formed,  giving  experimental  measures  of  refraction 
for  the  various  angles  of  incidence,  and  for  different  media, 
many  centuries  before  Snell,  in  1621,  superseded  the  use 
of  many  of  these  Tables  by  discovering  the  simple  Law 
of  Nature,  that  the  ratio  of  the  sines  of  the  angles  of 
incidence  and  those  of  refraction  is  constant  for  the 
same  medium.  Every  measurement  of  refraction  as  for- 
merly given  in  those  Tables  was  a  General  Fact,  includ- 
ing every  case  of  a  ray  of  light  falling  upon  the  given 
medium  at  the  given  angle ;  and  this  Fact  was  obtained, 
of  course,  by  reasoning  Inductively,  that  as  the  refraction 
for  this  angle  of  incidence  and  this  medium  had  been  ac- 
tually observed  to  be  of  this  magnitude  in  some  cases, 
(namely,  in  all  that  had  been  observed,)  it  would  be 
found  of  the  same  magnitude  in  all  such  cases.  Snell's 
discovery  of  the  "  Law  "  took  the  place  of  an  immense 
number  of  such  Facts,  by  summing  them  all  up  in  one 
general  proposition  or  formula,  thereby  rendering  any  de- 
tailed mention  of  them  unnecessary. 

Such  a  discovery  as  this  by  Snell  is  what  Dr.  Whewell, 
by  a  happily  selected  phrase,  calls  a  "  Colligation  of  Facts  " ; 
and  the  process  by  which  it  is  arrived  at  —  the  method,  if 
there  be  one,  of  making  such  a  discovery  —  is  what  he  de- 
nominates Induction.  Mr.  Mill  very  properly  objects,  that 
it  is  not  Induction  at  all.  It  is  an  act  of  generalization, 
founded  on  direct  intuition  of  the  relations  which  the  cases 
actually  before  us  bear  to  each  other,  and  not  professing  to 
extend  beyond  these  cases.  Consequently,  it  does  not  en- 
large our  knowledge,  as  Induction  always  does,  but  only 
grasps  up  together  into  one  Concept  the  knowledge  which 
we  already  possessed  ;  and  it  accomplishes  this  through 
perceiving  that  this  group  of  General  Facts,  instead  of 
being  entirely  heterogeneous,  as  they  at  first  appeared, 


408  INDUCTION  AND   ANALOGY. 

are  really  linked  together  by  some  common  relation,  the 
expression  of  which  reduces  them  to  unity  in  the  Under- 
standing, and  so  renders  them  more  easy  to  be  remem- 
bered and  more  convenient  to  be  used. 

It  is  true,  as  Mr.  Mill  remarks,  that  a  real  act  of  Induc- 
tion usually  goes  along  with  the  Colligation,  as  subsidiary 
to  it.  In  this  case,  Snell  not  only  took  for  granted  the 
previous  Inductions,  which,  as  we  have  seen,  are  expressed 
in  the  separate  General  Facts  that  he  grouped  together  in 
his  formula,  but  also,  having  ascertained  by  actual  observa- 
tion that  this  formula  held  true  for  refraction  in  some  media, 
he  reasoned  Inductively  that  it  would  hold  true  for  all 
media,  or,  in  other  words,  that  it  was  the  universal  Law 
of  refraction. 

It  ought  also  to  be  remarked,  that  the  discovery  of  the 
Law  which  colligates  the  General  Facts  does  not  change 
the  nature  of  the  evidence  on  which  those  Facts  depends, 
or  raise  them  out  of  the  rank  of  Probable,  into  that  of  De- 
monstrative, judgments.  These  Facts  are  still  nothing  but 
truths  of  Induction,  just  as  much  after  the  discovery  of  the 
Law  as  they  were  before  it.  The  discovery,  it  is  true, 
makes  the  previous  Inductions  somewhat  more  probable 
than  they  were  before ;  but  it  does  not  by  any  means  de- 
monstrate them.  The  degree  of  probability  is  increased 
through  the  discovered  consilience  of  the  Inductions,  as  this 
consilience  amounts  to  increasing  the  basis  of  enumera- 
tion on  which  each  of  them  rests.  A  number  of  conclu- 
sions affecting  a  group  of  kindred  subjects  are  mutually 
strengthened,  when  it  is  found  that  the  separate  Induction 
leading  to  each  one  of  them  harmonizes  in  one  respect, 
or  in  several  respects,  with  the  Inductions  leading  to  all 
the  others ;  for  such  harmony  is  precisely  what  we  expect, 
in  view  of  the  Maxim  on  which  all  Inductive  reasoning 
depends,  that  nature's  course  is  uniform.  Each  Induction 
stands  more  firmly,  when  it  not  only  rests  on  its  own  foun- 


INDUCTION   AND  ANALOGY.  409 

dation,  but  is  indirectly  supported  by  the  foundations  of  its 
neighbors. 

According  to  the  view  here  given,  a  Law  of  Nature  is  a 
generalization  of  the  second  order;  in  some  respects,  it 
bears  the  same  relation  to  General  Facts,  that  a  General 
Fact  bears  to  Individual  Facts.  I  say  "in  some  respects"; 
for  this  statement  does  not  convey  the  whole  truth.  A 
Law  of  Nature  is  not  a  mere  truth  of  classification ;  it  is 
not  merely  a  Genus  of  which  the  several  General  Facts  are 
the  Species.  If  it  were,  then  the  tabulated  measures  of 
refraction,  or  any  other  mere  collection  of  General  Facts 
relating  to  the  same  class  of  subjects,  might  be  called  a 
Law.  But  it  is  not  so ;  a  Law  may  be  contained  in  such 
a  Table,  but  it  is  concealed  there,  and  when  discovered, 
the  Table  itself  becomes  useless.  The  discovery,  as  I  have 
said,  consists  in  a  perception  of  the  truth,  that  the  group 
of  General  Facts  falls  naturally  into  a  series,  in  which  the 
place  or  power  of  any  term  is  easily  deduced  from  a  single 
brief  formula.  The  effort  of  mind  by  which  such  a  dis- 
covery is  made  is  rather  an  Intuition,  or  a  happy  conjec- 
ture, than  an  Induction.  The  kind  of  conviction  which 
attends  the  discovery,  when  made,  is  not  mere  probability, 
but  certainty.  With  reference  to  the  General  Facts  actu- 
ally before  us,  we  know  that  the  Law  is  there,  for  we  see  it 
just  as  soon  as  we  have  learned  where  to  look  for  it.  But 
the  universality  of  the  Law,  the  extension  of  it  to  all  other 
General  Facts,  not  now  observed,  of  the  same  class,  is  the 
result  of  an  Induction ;  and  the  establishment  of  the  Law 
also  tak^s  for  granted  the  validity  of  the  preceding  Induc- 
tions on  which  each  separate  General  Fact  depends.  Here, 
as  elsewhere,  whenever  we  attempt  to  extend  our  knowl- 
edge beyond  what  is  actually  observed,  our  only  guide  is 
Induction  by  simple  enumeration. 

The  process  of  hunting  for  a  Law  of  Nature  amid  a 
group  of  General  Facts  is  essentially  tentative,  resembling 

18 


410  INDUCTION  AND  ANALOGY. 

an  attempt  to  find  the  meaning  of  a  riddle ;  we  try  one 
guess  after  another,  and  at  last  stumble  upon  the  right  one 
when  we  least  expected  it.  Success  is  usually  obtained, 
not  by  trying  to  extend  the  survey,  or  to  contemplate  the 
largest  possible  number  of  cases,  but  by  restricting  the 
field  of  search  to  a  few  well-chosen  instances,  and  attempt- 
ing to  find  a  pattern  or  construction  which  these  few  will 
precisely  fit.  To  take  an  example  from  a  quarter  where 
we  should  least  expect  to  find  one,  —  from  pure  mathe- 
matics ;  Newton  discovered  the  Binomial  Theorem,  which 
is  a  true  Law  of  Nature  according  to  our  definition,  prob- 
ably by  simple  inspection  of  a  few  of  the  lower  powers  of 
binomials,  the  law  of  the  exponents  being  obvious  enough, 
and  that  of  the  coefficients  offering  but  little  difficulty  to 
his  marvellous  insight.  He  certainly  discovered  af!d  used 
the  Theorem  long  before  he  endeavored  to  demonstrate  it, 
or  to  trace  it  to  its  true  mathematical  principles.  There 
is  reason  to  believe  that  not  a  few  of  the  general  theorems 
of  the  higher  mathematics  have  been  discovered  in  a  pre- 
cisely similar  manner. 

Why  the  Law  should  be  suddenly  revealed  to  a  single 
happy  glance,  when  it  had  previously  escaped  the  most 
laborious  research,  is  a  curious  problem,  which  perhaps 
admits  of  no  complete  solution,  though  the  process  may 
be  elucidated  in  a  few  particulars.  The  essential  charac- 
teristic of  such  a  Law  is  a  series  proceeding  by  some  uni- 
form gradation,  the  relation  between  two  or  more  consecu- 
tive terms  in  any  part  of  it  being  the  same  as  that  existing 
between  the  corresponding  terms  in  any  other  part.  This 
relation  may  be  simple  or  complex,  recondite  or  obvious. 
Each  term  may  be  an  increment  of  its  predecessor  by  the 
addition  of  a  constant  quantity,  or  may  be  a  simple  multi- 
ple of  it,  or  may  be  related  to  it  through  some  of  the  peri- 
odic magnitudes  connected  with  a  varying  angle,  such  as 
the  sine,  tangent,  secant,  &c. ;  or  the  law  of  progression 


INDUCTION  AND   ANALOGY.  411 

may  be  covered  up,  as  it  were,  by  a  constant  quantity 
added  to  each  of  the  terms ;  or  the  numbers,  as  we  have 
them,  may  be  the  complex  results  of  two  or  more  indepen- 
dent series  multiplied  into  each  other,  in  which  case  there 
are  two  or  more  independent  Laws  to  be  discovered.  Two 
difficulties,  then,  are  to  be  overcome,  either  one  of  which 
would  seem  to  be  insuperable  if  the  other  had  not  been 
previously  mastered ;  we  must  properly  arrange  the  terms 
of  the  series  before  the  Law  of  it  can  be  discovered,  but  a 
knowledge  of  the  Law  is  indispensable  before  we  can  with 
certainty  make  such  an  arrangement.  In  a  contest  with 
so  many  and  so  serious  difficulties,  it  is  not  surprising  that 
success  at  last  should  often  seem  attributable  quite  as  much 
to  accident,  as  to  sagacity  and  dogged  perseverance. 

Kepler  has  furnished  an  instructive  narrative  of  his  suc- 
cessive attempts  to  reduce  to  Law  the  astronomical  obser- 
vations of  Tycho,  constructing-  many  formulae  by  hypothesis, 
finding  that  one  after  another  would  not  fit,  and,  after  each 
disappointment,  trying  again  with  unwearied  patience.  At 
last,  his  perseverance  was  rewarded  with  the  discovery  of 
the  great  Laws  which  deservedly  bear  his  name,  as  they 
are  the  foundations  of  the  whole  modern  science  of  astron- 
omy, for  they  sum  up  in  three  sentences  all  recorded  as- 
tronomical observations.  He  also  attempted,  in  a  similar 
way,  to  detect  the  Law  concealed  in  the  measured  angles 
of  refraction,  by  comparing  them  with  the  angles  of  inci- 
dence through  a  variety  of  constructions  by  triangles,  conic 
sections,  &c. ;  but  all  without  success.  Where  he  failed, 
Snell  succeeded,  twenty  years  later,  merely  by  turning  his 
attention  from  the  direct  measures  of  the  angles  to  the  ratio 
of  their  sines.  The  law  was  then  manifest  at  a  glance. 
Such  instances  are  needed  to  remind  us,  that  the  well- 
known  fable  of  Columbus  and  the  egg  is  not  a  caricature, 
but  a  faithful  representation,  of  many  of  the  greatest  dis- 
coveries  in   science.      What   Dr.  Whewell   happily  calls 


412  INDUCTION  AND  ANALOGY. 

"  the  ex-post-facto  obviousness  of  discoveries,  is  a  delusion 
to  which  we  are  liable  with  regard  to  many  of  the  most 
important  discoveries." 

The  validity  of  a  Law  of  Nature  thus  discovered,  as  it 
were,  by  a  happy  casualty,  is  regarded  as  sufficiently  estab- 
lished by  comparison  with  but  very  few  of  the  observed 
data  from  which  it  was  educed.  Thus,  Dalton's  magnifi- 
cent generalization,  coextensive  with  all  matter,  and  now 
verified  by  almost  countless  analyses,  that  chemical  ele- 
ments combine  only  in  definite,  reciprocal,  and  multiple 
proportions,  was  first  suggested  to  him  during  his  examina- 
tion of  only  two  compounds  ;  "  and  was  asserted  gener- 
ally," says  Dr.  Whewell,  "  on  the  strength  of  a  few  facts, 
being,  as  it  were,  irresistibly  recommended  by  the  clear- 
ness and  simplicity  which  the  notion  possessed."  What  is 
the  ground  of  this  bold  anticipation  of  the  universality  of  a 
Law  as  yet  verified  only  by  a  very  few  examples,  when,  in 
the  case  of  a  General  Fact,  as  already  shown,  a  very  ex- 
tensive Induction  may  still  leave  us  in  doubt  whether  the 
supposed  truth  may  not  be  contradicted  by  the  next  in- 
stance that  arises  ?  In  general  terms,  the  answer  is  obvi- 
ous. Simple  uniformities,  such  as  are  comprehended  in  a 
General  Fact,  may  be  merely  accidental ;  to  recur  to  an 
instance  already  cited,  all  ruminating  animals  now  known 
divide  the  hoof;  but  as  the  number  of  such  animals  is  not 
very  great,  this  simple  coincidence  of  two  properties  may 
be  as  casual  as  the  experience  of  an  individual  observer 
who  has  never  happened  to  see  a  squint-eyed  person  that 
had  not  also  brown  hair.  But  complex  uniformities,  such 
as  are  marshalled  into  the  symmetrical  series  called  Laws 
of  Nature,  and  thus  expressed  in  one  formula,  cannot  be 
regarded  as  accidental.  As  the  number  of  individual  facts 
comprehended  in  one  of  these  series  is  very  great,  it  is  in- 
credible that  mere  chance  should  throw  even  a  portion  of 
them  into  symmetrical  groups,  bearing  a  constant  ratio  to 


INDUCTION  AND  ANALOGY.  413 

each  other.  Hence,  if  we  can  detect  but  a  portion,  even  a 
fragment,  of  such  a  series,  we  feel  assured  that  it  will  prove 
to  be  continuous,  that  the  Law  will  not  change,  that  the 
uniformity  will  be  carried  out  to  the  end.  Only  the  action 
of  a  permanent  and  unvarying  Cause,  it  is  assumed,  could 
so  harmonize  results.  Nay,  so  strong  is  our  assurance  of 
the  universality  of  the  principle  thus  discovered,  though  it 
seems  as  yet  very  imperfectly  verified,  that,  when  an  anom- 
alous or  inconformable  instance  actually  arises,  we  seek  at 
once  for  the  means  of  eliminating  it,  or  explaining  it  away, 
instead  of  allowing  it  to  wrest  the  inchoate  discovery  out 
of  our  grasp  and  send  us  to  the  work  of  research  again. 
We  class  the  exception  immediately  among  those  apparent 
exceptions  which  really  confirm  the  rule ;  — just  as  we 
now  see  that  the  rising  of  a  balloon  in  the  atmosphere  does 
not  contradict,  but  actually  verifies,  the  Law  of  gravita- 
tion. 

We  come,  then,  to  the  conception  of  a  physical  Cause,  as 
indicating  the  third  or  highest  stage  in  the  generalizations 
of  science,  and  therefore  as  bearing  the  same  relation  to  a 
Law  of  Nature,  that  such  a  Law  bears  to  a  General  Fact. 
As  thus  understood,  a  Cause  is  simply  a  higher  Law,  un- 
der which  several  inferior  Laws  are  subsumed ;  it  appears 
as  the  original  principle,  of  which  these  lower  Laws  are 
the  derivatives  by  immediate  and  necessary  consequence. 
Thus,  the  theory  of  gravitation,  or  the  doctrine  that  every 
body  attracts  every  other  body  with  a  force  which  is  di- 
rectly as  its  mass  and  inversely  as  the  square  of  its  dis- 
tance, is  the  statement  of  a  universal  principle,  under  which 
not  only  Kepler's  Laws  of  the  planetary  motions,  but  the 
Laws  of  falling  bodies,  of  the  equilibrium  of  fluids,  &c,  are 
subsumed  in  this  sense  ;  —  that  if  we  take  for  granted  the 
existence  of  the  force  or  physical  Cause,  termed  Gravity, 
which  this  theory  assumes,  then  these  inferior  Laws  may 
all  be  deduced  from  it  by  Demonstrative  Reasoning.     That 


414  INDUCTION  AND   ANALOGY. 

such  Deduction  is  possible,  is  the  only  proof  we  have  that 
such  a  force  or  Cause  exists.  The  hypothetical  force,  for  it 
is  nothing  more,  represents  the  inferior  Laws  that  are  sub- 
sumed under  it,  merely  because  it  is  an  expression  of  them 
in  a  single  formula.  It  may  well  happen  that  two  or  more 
such  formulas  may  be  devised,  differing  essentially  from 
each  other,  yet  answering  equally  well  all  the  conditions 
of  the  case,  as  the  given  Laws  may  logically  be  deduced 
from  either  of  them.  For  instance :  —  all,  or  the  greater 
part,  of  the  Laws  of  vision  and  light  may  be  explained  with 
equal  precision  and  accuracy  either  on  the  doctrine  of  emis- 
sion, or  on  the  undulatory  theory.  Two  such  hypotheses 
correspond  to  two  very  dissimilar  engines,  which  different 
mechanics  might  invent,  in  order  to  cause  the  hands  of  a 
clock  to  make  the  required  movements  over  the  dial-plate, 
or  the  little  balls  in  an  orrery  to  counterfeit  the  motions  of 
the  solar  system.  It  is  no  more  necessary  to  suppose  that 
such  an  attractive  force  as  Gravity,  or  such  a  luminiferous 
ether  as  the  undulatory  theory  treats  of,  actually  exists, 
than  it  is  to  believe  that  a  set  of  wheels  and  pinions,  like 
that  which  moves  an  orrery,  really  produces  the  motion  of 
the  planets.  All  that  the  theory  does  for  us  is  to  represent 
the  phenomena  correctly;  no  one  who  understands  the 
subject  supposes  that  the  hypothetical  force  or  Cause,  which 
is  merely  a  convenient  supposition  for  the  theorist,  actually 
produces  those  phenomena. 

It  is  evident  that  such  Causes  as  we  are  now  speaking 
of  are  merely  the  highest  generalizations  of  Physical  Sci- 
ence, and  that  the  invention  of  them  —  for  they  are  rather 
invented  than  discovered — affords  not  the  slightest  addi- 
tional evidence  of  the  universality  of  those  Laws  of  Nature 
which  they  represent,  or  which  are  subsumed  under  them. 
The  proof,  indeed,  proceeds  in  the  opposite  direction  ;  the 
only  evidence  we  have  that  the  right  Cause  has  been  as- 
signed is,  that  it  correctly  represents  the  Laws  which  are 


INDUCTION  AND  ANALOGY.  415 

placed  under  it.  When  it  is  demonstrated  that  the  Law 
may  be  deduced  from  such  a  Cause,  the  real  course  of  the 
argument  is,  from  the  admitted  validity  of  the  Conclusion 
to  infer  the  soundness  of  the  Premise.  Gravity  does  not 
cause  heavy  bodies  to  fall  to  the  ground,  nor  does  it  bind 
the  planets  to  their  orbits ;  but  Gravity  is  rightly  consid- 
ered as  a  "  physical  Cause,"  in  the  technical  sense  of  that 
phrase,  because  its  hypothetical  existence  enables  us  cor- 
rectly to  represent  in  a  single  formula  the  phenomena  of 
falling  bodies  and  of  the  planetary  motions. 

The  higher  generalizations,  then,  depend  exclusively,  for 
proof  of  their  correctness,  on  the  validity  of  those  which  are 
next  below  them.  When  the  proper  Law  of  Nature  is 
provisionally  assumed,  certain  consequences  can  be  demon- 
strated to  follow  which  agree  with  the  General  Facts  that 
were  previously  established  on  Inductive  evidence ;  when 
the  proper  physical  Cause  is  assumed,  we  can  logically 
make  certain  Deductions  from  it  which  harmonize  with  the 
Laws  of  Nature  which  this  Cause  was  invented  to  express. 
Neither  the  Law  nor  the  Cause  brings  any  additional  evi- 
dence of  its  own,  but  both  alike  depend  for  proof,  in  the 
last  analysis,  on  the  validity  of  the  Induction  by  simple 
enumeration  by  which  we  first  collected  their  common 
basis,  the  General  Facts.  The  process  of  verifying  both 
consists  in  enlarging  the  Induction,  but  not  in  altering  its 
character ;  both  the  Law  and  the  Cause  being  assumed  to 
be  universally  true,  we  make  further  Deductions  from 
them,  and  still  find  these  to  coincide  with  the  observed 
Facts.  In  other  words,  we  first  reason  Inductively  from 
some  to  all,  and  then,  assuming  provisionally  that  the  prin- 
ciple holds  true  of  all,  we  reason  from  it  Deductively  to 
other  some,  and  find  that  these  also  are  confirmed  by  obser- 
vation, so  that  they  reflect  evidence  upon  the  Law  or  the 
Cause  of  which  they  are  the  logical  consequences.  Turn 
the  matter  as  we  may,  Induction  by  simple  enumeration  is 


416  INDUCTION  AND  ANALOGY. 

still  the  basis  of  the  whole  procedure,  and  the  discovery  or 
invention  of  Laws  of  Nature,  or  physical  Causes,  only  sup- 
plies names  and  formulas  of  expression  for  the  successive 
steps  of  generalization,  as  we  form  one  after  another  the 
proper  hierarchy  of  Concepts. 

We  can  now  see  more  plainly  than  before  the  correct- 
ness of  the  doctrine  already  advanced,  that  the  strong  and 
unhesitating  belief  which  we  accord  to  any  well-established 
Law  of  Nature,  and  which  we  indicate  by  saying  that  an 
event  happening  under  it  takes  place  by  a  physical  neces- 
sity, is  not  due  to  the  strength  of  the  Induction  through 
which  the  Law  was  discovered,  but  to  our  absolute  a  'priori 
conviction  of  the  fixedness  of  the  relation  which  connects 
every  effect  with  its  efficient  Cause.  The  Law  is  discovered 
by  Induction  ;  but  it  is  proved  by  a  different  process,  —  by 
bringing  it  under  a  necessary  a  priori  conception  of  the 
human  mind,  that  of  Efficient  Cause,  and  thereby  subject- 
ing it  to  the  principle  of  Causality,  that  every  event  must 
have  a  Cause,  and  must  be  proportional  to  that  Cause. 

In  speaking  of  the  use  which  is  sometimes  made  of  In- 
ductive reasoning  in  pure  mathematics,  as  in  the  case  of 
Newton's  discovery  of  the  Binomial  Theorem,  Mr.  Mill 
maintains  that  the  process  of  thought  in  such  cases  is  not 
an  Induction  properly  so  called,  but  is  governed  by  certain 
"  a  priori  considerations  (which  might  be  exhibited  in  the 
form  of  demonstration),  that  the  mode  of  formation  of  the 
subsequent  terms,  each  from  that  which  preceded  it,  must 
be  similar  to  the  formation  of  the  terms  which  have  been 
already  calculated."  But  it  was  certainly  Inductive  in  this 
respect,  that  the  observed  regular  formation  of  the  first  few 
terms  of  the  series  originally  led  Newton  to  anticipate  that 
all  the  other  terms  must  be  formed  in  the  same  manner, 
and  to  act  upon  this  anticipation,  —  that  is,  confidently  to 
use  the  Theorem  for  a  long  time,  —  without  giving  himself 
the  trouble  to  work  out  a  demonstration  of  it.     Undoubt- 


INDUCTION  AND   ANALOGY.  417 

\  dJy  he  had  a  strong  belief  that  such  a  demonstration  was 
practicable ;  and  this  belief  prompted  him  to  acquiesce  with 
greater  confidence  in  the  result  of  the  Induction.  For  this 
very  reason,  this  instance  appears  to  be  a  typical  and  in- 
structive case  of  Inductive  reasoning.  Pure  Induction  is 
exclusively  an  organon  of  discovery,  a  clew  for  anticipating 
facts  not  yet  observed  and  truths  not  yet  proved.  The 
Ground  of  the  Induction,  that  is,  the  proof,  if  it  may  be 
called  such,  or  the  source  of  the  confidence  with  which  we 
accept  its  conclusions,  is  an  indistinct  assurance,  derived 
from  a  priori  considerations,  that  the  results  might  be  de- 
monstrated, if  we  were  acquainted  with  all  the  circumstances 
of  the  case.  Newton's  assurance  was  founded  on  his  indis- 
tinct anticipation  of  the  truth,  that  the  formation  of  the  co- 
efficients of  the  series  must  depend  in  some  manner  on  the 
laws  of  the  permutation  and  combination  of  numbers, — 
an  anticipation  which  he  did  not  stop  to  work  out  and 
verify.  The  physicist's  assurance  is  based  primarily,  as 
we  have  seen,  on  his  necessary  conviction  that  every  event 
or  v  change  must  have  an  efficient  Cause,  a  truth  which 
is  readily  explicated  into  the  maxim  that  Nature's  course 
is  uniform  ;  and  secondarily,  upon  his  belief  that  the  pro- 
portional variation  of  the  successive  terms  in  such  a  se- 
ries as  is  called  a  Law  of  Nature  is  another  consequence 
of  the  axiomatic  principle  of  Causality,  that  effects  must  be 
proportional  to  their  Causes.  The  physicist's  anticipation 
cannot  be  verified,  because,  in  the  physical  universe,  Effi- 
cient Causes  lie  beyond  the  reach  of  human  insight.  We 
can  discover  nothing  but  Invariable  Antecedents.  But  so 
strong  is  the  bias  which  leads  us  to  identify  an  Invariable 
Antecedent  with  an  Efficient  Cause,  that  the  phraseology 
of  Causation  is  still  employed  throughout  our  investigations, 
though  it  has  been  demonstrated  over  and  over  again,  that 
constancy  of  sequence  is  no  certain  indication  of  causal 
efficiency.      We  still  speak  of  physical   Causes,  of  agents 

18*  AA 


418 


INDUCTION  AND  ANALOGY. 


and  their  action,  of  forces  and  powers,  although  it  is  now 
admitted  on  all  hands  that  we  mean  nothing  by  such 
language,  when  employed  with  reference  to  the  material 
universe,  except  "constant  relations  of  succession  or  of 
similarity."  The  very  persistency  of  this  inappropriate 
phraseology  indicates  quite  clearly  the  source  of  our  con- 
\iction  that  Nature's  course  is  uniform,  and  her  Laws  un- 
changeable, except  by  Him  whose  infinite  wisdom  first 
established  them,  and  whose  unvarying  purposes  and  modes 
of  action  they  express. 


SOURCES   OF  EVIDENCE  AND   CAUSES   OF  ERROR.         419 


CHAPTER    XIII. 

THE  SOURCES   OF  EVIDENCE  AND  THE  CAUSES  OF  ERROR. 

INTUITION  is  not  only  the  source  in  which  all  oui 
knowledge  originates,  but  it  is  the  universal  basis  of 
certainty,  or  the  sole  ground  of  the  confidence  with  which 
we  accept  any  facts  or  truths  as  known.  What  we  directly 
or  immediately  perceive,  whether  by  the  external  senses 
or  by  consciousness,  that  we  know.  What  is  not  thus  di- 
rectly perceived  is  entitled  to  be  called  knowledge  only  in  a 
secondary  or  derivative  sense ;  properly  speaking,  it  is  only 
an  inference  from  our  knowledge,  and  however  legitimate 
this  Inference  may  be,  it  is  worth  nothing  if  the  truth  of 
one  or  more  Intuitions,  on  which  it  depends,  be  not  previ- 
ously taken  for  granted.  Take  even  Demonstrative  Rea- 
soning, for  instance,  in  which  it  is  rightly  said  that  the 
Conclusion  is  a  necessary  inference  from  the  Premises. 
Still,  before  we  can  accept  this  Conclusion  as  certain,  we 
must  assume  that  both  the  Premises  are  true.  Now,  what- 
ever be  the  nature  of  the  Major  Premise,  the  Subsumption 
must  express,  either  directly  or  indirectly,  a  truth  of  Intui- 
tion. We  can  knowingly  assert  that  a  given  object  pos- 
sesses a  certain  attribute,  or  bears  a  certain  relation  of  like- 
ness or  unlikeness  to  some  other  object,  only  through  our 
direct  perception  of  this  fact  either  by  sense  or  conscious- 
ness ;  and  such  an  assertion  must  enter  into  every  act  of 
Reasoning,  as  one  of  the  grounds  on  which  the  Conclusion 
rests.  Any  Reasoning,  then,  by  which  we  might  attempt 
to  doubt  or  deny  the  validity  of  our  Intuitions,  would  be 


420  THE   SOURCES   OF  EVIDENCE 

self-destructive ;  for  in  such  Reasoning,  the  truthfulness  of 
our  Intuitive  faculties  must  be  presupposed,  or  taken  for 
granted.  We  should,  by  such  scepticism,  deny  the  legiti- 
macy of  our  own  denial. 

Intuition,  therefore,  is  the  highest  source  of  evidence, 
and  the  ultimate  foundation  of  all  certainty.  If  we  can- 
not accept,  as  absolutely  true,  what  we  immediately  per- 
ceive, or  are  conscious  of,  then  we  can  know  nothing ;  we 
cannot  even  know  that  we  do  not  know.  But  before  we 
place  this  absolute  reliance  upon  Intuition  or  Perception, 
we  must  carefully  distinguish  what  it  is  that  we  really  per- 
ceive, or,  in  other  words,  what  that  is  of  which  we  have 
an  Intuition.  In  ordinary  mental  action,  Inferences  are  so 
quickly  and  habitually  drawn  from  Intuitions,  and  thereby 
so  closely  blended  with  them,  acts  of  comparison  and  gen- 
eralization also  entering  into  the  compound  result,  that  it 
becomes  extremely  difficult  to  separate  the  pure  Matter  of 
Intuition,  of  which  we  are  absolutely  certain,  from  the 
heterogeneous  ingredients  which  are  thus  united  with  it, 
and  of  which  we  are  not  by  any  means  equally  sure. 
Hence  it  is  often  said  that  our  senses  deceive  us,  when 
the  truth  is,  that  we  are  mistaken  only  in  the  Inferences 
which  we  have  incorrectly  drawn  from  the  data  actually 
furnished  by  the  senses.  Thus  we  are  often  deceived  into 
accepting  a  counterfeit  as  a  good  coin ;  but  the  mental  act 
which  thus  leads  us  into  a  mistaken  belief  is  really  com- 
pound, embracing  an  act  of  memory,  one  of  generaliza- 
tion, and  one  of  Reasoning.  The  little  object  placed  in 
our  hands  for  examination  is  perceived  to  have  a  certain 
color,  weight,  shape,  stamp,  &c. ;  and  it  is  impossible  that 
these  qualities  should  be,  to  us,  in  any  respect  different  from 
what  they  are  perceived  to  be.  But  when  we  proceed  to 
compare  these  qualities  with  others  which  we  remember  to 
have  perceived  at  some  other  time  in  good  coins,  and  to 
infer  from  their  similarity  that  this  supposed  coin  is  not  a 


AND  TIIE   CAUSES   OF  ERROR.  421 

counterfeit,  it  is  evident  that  we  are  exposed  to  many 
sources  of  error.  Even  if  we  go  so  far  only  as  to  desig- 
nate one  of  these  qualities  by  its  Common  Name,  —  to  say, 
for  instance,  that  tliis  coin  is  yellow,  —  we  go  beyond  the 
Intuition,  and,  so  far,  become  liable  to  mistake ;  it  may  well 
be  that  we  have  but  an  imperfect  recollection  and  imagi- 
nation of  the  color  which  is  usually  so  called,  and  therefore 
may  be  mistaken  in  supposing  that  this  color  is  so  similar 
to  it  as  to  merit  the  same  name.  In  like  manner,  any 
other  comparison,  as  of  the  weight,  shape,  or  stamp,  as  it 
requires  either  memory,  if  both  objects  be  not  actually  be- 
fore us,  or  a  decision  as  to  the  degree  of  similarity,  if  they 
are  both  present  to  sense,  must  involve  an  element  of  un- 
certainty. 

The  question  has  been  raised,  whether  external  objects 
are  directly  perceived  by  us  as  external,  or  whether  their 
externality  is  an  Inference  subsequently  drawn  from  this 
perception  as  combined  with  others,  and  as  governed  by 
the  necessary  and  a  priori  convictions  of  the  mind.  In 
other  words,  is  the  externality  of  the  object,  or  the  fact 
that  it  is  something  different  from  myself,  that  it  is  not-me, 
a  constituent  part  of  the  Intuition,  or  only  an  Inference 
from  it?  If  the  former  supposition  be  true,  then  I  know 
that  the  external  world  exists,  and  any  Reasoning  upon  the 
case,  either  for  or  against  this  knowledge,  is  superfluous, 
and  even  illogical ;  for  as  Reasoning  must  involve  and  de- 
pend upon  Intuition,  it  cannot  contradict  Intuition.  But 
if  the  latter  supposition  be  correct,  then  the  reality  of  the 
outward  universe  is  not,  strictly  speaking,  known,  but  only 
inferred  through  an  act  of  the  understanding,  which,  as  it 
purports  to  relate  to  real  objects,  and  not  to  a  mere  con- 
ception of  the  mind,  certainly  may  be  a  mistaken  one. 

The  question  is  an  important  one,  but  the  full  discussion 
of  it  belongs  to  Metaphysics,  and  not  to  Logic.  We  can 
only  considei  here  the  nature  and  the  relevancy  of  the  evi- 


422  THE   SOURCES   OF  EVIDENCE 

dcnce  adduced,  regarded  as  illustrating  the  general  laws  of 
evidence.  Thus  much,  I  think,  must  be  admitted,  that 
the  mind,  in  its  adult  state,  is  immediately  conscious  of  the 
affections  of  its  own  bodily  organism  as  such,  —  that  is,  as 
affections  of  the  body,  which  is  foreign  to  itself,  or  a  part 
of  the  not-me  ;  for  we  localize  these  affections,  or  refer  them 
instantly,  and  without  an  act  of  reasoning,  to  the  affected 
parts.  Thus,  I  am  immediately  conscious  of  a  pain,  not 
merely  as  a  pain,  but  as  a  pain  in  the  foot,  in  the  hand,  or 
in  the  head,  the  Intuition  extending  to  the  locality,  just  as 
much  as  to  the  severity,  of  the  affection.  But  it  is  said 
that  the  pain,  being  a  sensation,  can  exist  only  in  the  sen- 
tient mind,  and  not  in  the  unsentient  matter  of  the  body. 
Very  true ;  but  the  question  then  arises,  Where  is  the  mind  ? 
You  have  no  right  to  confine  it  to  a  certain  part  of  the 
body,  —  to  the  brain,  for  instance.  I  say,  that  the  mind  is 
wherever  it  feels;  for  its  feeling  —  its  state  of  consciousness 
—  is  the  only  evidence  that  we  have  of  its  existence.  It 
is  present,  at  least,  to  the  whole  nervous  organism.  As  we 
certainly  feel  at  the  tips  of  our  fingers,  it  is  little  more  than 
tautology  to  assert,  that  that  which  feels  is  existent  at  the 
tips  of  the  fingers.  It  is  admitted  that  this  doctrine  of  the 
ubiquity  of  the  mind  to  the  body  is  incomprehensible ;  we 
cannot  see  how  it  is  that  the  thinking  being  should  be  "  all 
in  every  part "  of  its  extended  nervous  organism.  In  like 
manner,  many  physical  facts,  especially  those  of  electricity 
and  magnetism,  and  whatever  involves  the  action  of  what 
are  called  Polar  Forces,  are  inconceivable ;  but  this  is  no 
reason  for  doubting  their  reality,  when  they  are  evidenced 
by  Intuition.  But  if  the  mind  immediately  localizes  its 
sensations,  if  it  perceives  that  the  pain  is  here,  and  not 
there,  then  it  is  immediately  conscious  of  its  own  body  as 
extended,  and  therefore  of  space  and  externality. 

This  is  a  mere  outline  of  Sir  William  Hamilton's  doc- 
trine of  our  immediate  perception,  or  consciousness,  of  the 


AND  THE  CAUSES  OF  ERROR.  423 

external  world.  It  appears  to  disprove  very  satisfactorily 
Kant's  counter  assertion,  that  space  is  wholly  subjective, 
—  a  mere  law  of  our  perceptive  faculty,  which  imposes 
the  modes  of  its  own  being  upon  the  constitution  of  the 
objects  which  it  perceives.  But  while  the  Hamiltonian 
doctrine  seems  to  hold  good  of  the  adult  mind,  it  is  not  so 
clear  that  it  would  apply  to  the  perceptions  of  an  infant. 
It  may  be  questioned  whether,  at  the  dawn  of  our  exist- 
ence, our  sensations  are  distinctly  referred  to  outward 
things,  or  that  the  perceptions  by  which  they  are  accom- 
panied appear  to  be  anything  else  than  states  of  our  own 
consciousness.  An  infant's  world,  it  may  be  suspected, 
lies  entirely  within  himself;  and  if  so,  the  subsequent 
reference  of  these  perceptions  to  external  realities  must 
be  produced,  or  aided,  by  experience  and  an  act  of  Reason- 
ing, and  the  knowledge  or  belief  thus  gained  is  no  longer 
exclusively  Intuitive. 

Passing  over  this  metaphysical  question,  however,  it  is  to 
be  observed  that  Memory,  as  a  source  of  evidence,  stands 
next  in  extent  and  importance  to  Intuition.  In  many  cases, 
the  two  ar  so  closely  interwoven  with  each  other,  as  we 
have  just  seen,  that  facts  are  often  loosely  said  to  be  Intui- 
tively known,  when  we  have  no  better  evidence  of  their 
existence  than  is  afforded  by  Memory.  Intuition,  as  such, 
is  always  present,  relating  only  to  what  exists  now  and 
here ;  past  Intuitions  can  be  now  known  to  us  only  by  an 
act  of  remembrance  ;  and  as  the  strength  of  a  chain  is  the 
strength  of  its  weakest  link,  that  which  we  did  know  Intui- 
lively,  can  be  now  accepted  only  on  the  strength  of  our  be- 
lief that  we  remember  rightly.  In  like  manner,  when  we 
are  judging  of  Individual  Objects  by  comparison,  or  are 
ascertaining  their  relations  to  each  other,  or  to  a  class  of 
cognate  Objects,  the  results  of  the  observation  will  not  be 
Intuitively  certain,  unless  all  the  related  objects  are  pres- 
ent, at  one  and  the  same  moment,  either  to  sense  or  con- 


424  THE   SOURCES   OF  EVIDENCE 

sciousness ;  if  all  are  not  thus  present,  then,  to  the  extent 
of  this  deficiency,  objects  actually  observed  must  be  com- 
pared with  those  which  are  merely  remembered.  More- 
over, as  Locke  and  Dugald  Stewart  have  remarked,  even 
in  mathematical  demonstration,  we  have  not,  at  every  step, 
the  immediate  evidence  of  Intuition,  but  only  that  of 
Memory.  The  whole  science  of  geometry  hangs  together 
by  a  continued  chain  of  Intuitive  judgments ;  but  in  the 
case  of  any  advanced  theorem,  it  is  not  to  be  supposed  that 
we  can  carry  in  mind,  as  simultaneously  present  to  con- 
sciousness, all  the  truths,  previously  established,  which  must 
concur  in  order  to  support  this  particular  demonstration. 
In  by  far  the  greater  number  of  instances,  we  trust  entirely 
to  judgments  resting  on  the  evidence  of  Memory.  At  the 
close,  before  we  can  accept  the  Conclusion  as  demonstrated, 
we  must  remember  the  whole  chain  so  perfectly  as  to  be 
sure  that  nothing  has  been  left  out ;  we  must  recollect  not 
only  that  we  have  proved,  but  how  we  proved,  each  point. 
Practically,  then,  the  truths  of  geometry,  and  all  other 
Conclusions  dependent  on  a  chain  of  Demonstrative  Rea- 
soning consisting  of  more  than  two  or  three  links,  must  be 
accepted  on  the  evidence  of  Memory  quite  as  much  as  on 
that  of  Intuition.  Of  course,  the  Inductive  Sciences,  in- 
cluding, as  they  do,  a  vast  collection  of  facts,  are  dependent, 
to  a  still  greater  extent,  upon  this  source  of  evidence. 

But  the  edifice  of  Science,  when  it  is  thus  shown  to  be 
largely  dependent  upon  individual  recollections,  would  seem 
to  rest  on  a  very  insecure  basis.  The  defects  of  Memory, 
as  every  one  is  aware,  are  both  numerous  and  grave.  It 
is  capricious,  it  often  fails  us  when  we  most  need  its  aid, 
and  it  exists  in  very  different  degrees  in  different  persons. 
We  might  be  tempted,  at  the  first  glance,  to  pronounce  it 
cne  of  the  most  untrustworthy  of  all  our  faculties.  But  on 
closer  observation,  it  will  appear  that  the  faults  with  which 
it  is  chargeable  are  not  so  serious  as  we  might  at  first  sup- 


AND   THE  CAUSES   OF  ERROR.  425 

pose,  and,  especially,  that  they  do  not  much  diminish  its 
usefulness,  or  the  confidence  which  we  place  in  it,  as  an 
indispensable  means  for  the  progress  of  Science.  In  the 
first  place,  its  faults  are  rather  negative  than  positive  in 
character  ;  we  often  forget,  but  we  are  very  seldom  mis- 
taken in  what  we  think  that  we  distinctly  remember.  In 
truth,  a  remembrance,  seemingly  clear  and  distinct,  of 
what  we  have  but  recently  observed,  especially  if  the  phe- 
nomenon be  of  a  simple  and  definite  character,  must  be 
placed  next  to  Intuition  as  a  ground  of  certainty.  The 
distinction  between  a  pure  Intuition  now  present  to  the 
mind,  and  a  distinct  recollection  of  a  very  recent  one,  ex- 
perienced perhaps  within  the  last  hour,  is  theoretical  rather 
than  practical.  In  the  ordinary  conduct  of  life,  no  one 
would  think  of  maintaining  that  the  former  was  more  trust- 
worthy than  the  latter.  Our  judicial  tribunals,  in  grave 
matters  involving  property  and  life,  will  not  allow  the  clear 
and  distinct  recollections  of  a  witness,  though  extending 
over  a  much  longer  period,  to  be  even  called  in  question. 
Still,  the  theoretical  distinction  exists ;  Intuition,  as  the 
basis  of  Demonstration,  has  absolute  or  logical  certainty, 
and  does  not  admit  of  degrees  ;  while  Memory  is  confess- 
edly subject  to  error,  and  therefore  is  a  source  only  of 
•probable  evidence,  though,  in  its  highest  degree,  it  amounts 
to  what  is  called  moral  certainty. 

And  here  another  distinction  must  be  drawn.  We  must 
distinguish,  as  Hamilton  has  done,  between  the  simple  fact 
that  we  do  remember,  or  think  that  we  remember,  a  cer- 
tain phenomenon,  and  the  truthfulness  of  this  act  of  re- 
membrance, or  our  belief  in  the  former  actual  existence  of 
that  phenomenon.  The  former  is  matter  of  direct  Intui- 
tion, and  therefore  does  not  admit  of  doubt ;  the  latter  rests 
merely  upon  probable  evidence,  and  may  be  a  mistaken  be- 
lief. Memory  may  be  compared  to  a  witness  giving  testi- 
mony in  a  court  of  justice  ;    the  judge  and  jury  cannoi 


426  THE  SOURCES   OF  EVIDENCE 

doubt  that  he  does  testify  to  this  or  that  occurrence,  for 
they  have  sensible  —  that  is,  Intuitive  —  evidence  of  the 
fact ;  but  they  may  well  doubt  whether  he  testifies  truly,  — 
whether  the  occurence  in  question  ever  took  place.  It  is 
only  in  this  last  respect,  the  correctness  of  the  representa- 
tion of  what  we  remember,  that  the  faculty  of  Memory  is 
said  to  be  a  source  of  merely  probable  evidence. 

It  is  to  be  observed  that  the  art  of  writing  is  a  most  val- 
uable auxiliary  to  the  faculty  of  Memory,  inasmuch  as  a 
proper  use  of  it  may  obviate,  in  great  part,  the  uncertainty 
that  wou*d  otherwise  attach  to  this  source  of  evidence. 
Remembrance  is  more  perfect,  that  is,  more  clear  and  dis- 
tinct, and  thus  more  trustworthy,  according  as  the  Intui- 
tions which  it  preserves  and  stores  up  are  more  recent. 
But  a  written  record  of  the  observations,  taken  at  the 
time  when  they  were  made,  or  as  soon  afterwards  as  might 
be,  keeps  the  evidence  as  perfect  as  it  would  be  if  Mem- 
ory were  not  liable  to  be  impaired  by  the  lapse  of  time. 
The  possession  of  such  a  record  may  enable  even  future 
generations  to  accept  the  evidence  of  the  occurrence  with 
as  full  confidence  as  if  it  had  been  observed  by  their  con- 
temporaries only  a  few  days,  or  a  few  hours,  before.  Of 
course,  the  age  and  genuineness  of  the  document  must  first 
be  proved,  just  as  we  must  first  establish,  on  satisfactory 
grounds,  the  veracity  and  competency  of  the  witnesses  who 
testify  to  contemporary  events  which  we  have  not  ourselves 
observed.  But  this  being  done,  and  it  is  generally  about 
as  easy  to  do  in  the  one  case  as  in  the  other,  the  evidence 
remains  as  perfect  after  the  lapse  of  centuries  as  it  was  at 
the  time  when  the  record  was  made.  Time  is  thus  de- 
prived of  its  power  to  wipe  out  by  degrees  the  recollection 
of  events.  Many  facts  in  history,  though  of  very  old  date, 
must  be  admitted  to  be  now  as  firmly  established  as  if  they 
had  taken  place  within  the  lifetime  of  the  present  genera- 
tion.    Thus,  the  fact  that  a  deed  of  privileges,  called  the 


AND  THE  CAUSES  OF  ERROR.  427  '. 

Great  Charter,  was  granted  by  King  John  to  the  English 
people,  June  5,  1215,  is  even  now  as  firmly  established  as 
that  of  the  passage  of  the  Reform  Bill  in  1832 ;  and  the 
precise  nature  and  extent  of  the  franchises  granted  are  as 
fully  known  in  the  former  case  as  in  the  latter,  for  in  both 
cases  the  original  parchment  rolls,  on  which  these  title- 
deeds  of  freedom  were  first  engrossed,  and  attested  by  the 
seals  and  signatures  of  those  who  were  parties  to  them,  are 
yet  extant. 

We  dwell  upon  this  point  as  one  of  some  importance,  be- 
cause it  has  been  wrongly  maintained,  in  reference  to  what 
may  be  called  the  historical  part  of  Christianity,  that  as  the 
mere  lapse  of  time  slowly,  but  surely,  wears  away  all  his- 
torical evidence,  the  great  facts  on  which  our  religious  faith 
depends  must  become  subject  in  future  centuries  to  so 
much  uncertainty  as  to  be  wholly  unworthy  of  credit. 
The  proper  answer  to  this  assertion  is,  that  nothing  less 
than  a  general  conflagration,  which  should  burn  up  all  the 
written  and  printed  records  now  in  existence,  could  make 
these  facts,  to  any  appreciable  extent,  less  certain  thousands 
of  years  hence,  than  they  are  at  the  present  day.  Miracles 
were  needed  for  the  first  establishment  of  Christianity ;  but 
only  the  ordinary  course  of  God's  providence  is  necessary 
to  preserve  its  blessings  to  any  number  of  future  genera- 
tions. 

The  two  faculties  of  Intuition  and  Memory  are  the 
sources  only  of  our  individual  experience.  But  the  ex- 
perience of  an  individual  —  what  I  have  myself  observed 
and  remembered,  or  reduced  to  writing  —  is  extremely 
limited,  when  compared  with  the  vast  fund  of  information 
that  is  opened  to  us  by  accepting  the  experience  of  our  fel- 
low-men, and  combining  it  with  our  own.  Not  merely  in 
our  labors  for  the  advancement  of  Science,  but  in  the  or- 
dinary management  of  our  e very-day  concerns,  we  are 
obliged  to  depend  upon  the  Testimony  and  the  Authority 


428  THE  SOURCES  OF  EVIDENCE 

of  others.  Science  grows  by  a  combination  of  the  labors 
of  many  minds  and  a  long  succession  of  generations.  The 
lifetime  of  an  individual  might  be  spent  in  a  vain  endeavor 
to  review,  and  verify  by  personal  observation,  all  the  data 
which  support  the  conclusions  in  but  one  of  its  depart- 
ments. Many  of  them,  from  the  nature  of  the  case,  can- 
not be  so  verified ;  the  occurrences  of  former  times,  and 
even  those  in  our  own  day  that  took  place  under  a  pecu- 
liar combination  of  circumstances,  such  as  may  never  be 
repeated,  must  be  received  on  the  Testimony  of  others,  or 
be  left  entirely  out  of  account,  together  with  all  the  con- 
clusions that  are  founded  upon  them.  We  must  contin- 
ually accept  on  trust  what  others  have  observed,  and  even 
the  Inferences  that  they  have  drawn,  without  pretending 
to  verify  them  for  ourselves,  or  we  must  sit  down  in  igno- 
rance. And  this  remark  is  applicable  not  merely  to  the 
Inductive,  but  also  to  the  Exact  Sciences.  In  astronomi- 
cal calculations,  for  example,  very  few  of  the  data  rest 
upon  the  evidence  of  our  own  senses,  and  we  compute  by 
the  aid  of  a  book  of  logarithms,  the  accuracy  of  which,  at 
the  present  day,  no  one  thinks  of  verifying  by  independent 
calculation. 

Testimony  and  Authority  ought  to  be  sharply  distin- 
guished from  each  other,  though  they  are  often  loosely  used 
as  synonymous.  Properly  speaking,  we  accept  Testimony 
as  to  matters  of  fact,  and  yield  to  Authority  in  matters  of 
opinion.  Our  confidence  in  the  former  depends  mainly  on 
our  opinion  of  the  veracity  of  our  informant ;  in  the  latter 
case,  we  rely  chiefly  on  the  soundness  of  his  judgment,  the 
accuracy  of  his  habits  of  reasoning,  and  the  largeness  of 
his  information.  We  disbelieve  Testimony,  we  reject  Au- 
thority. The  reason  why  these  two  sources  of  belief  are 
so  frequently  confounded  is,  that  the  provinces  of  observa- 
tion and  of  reasoning  are  not  kept  sufficiently  distinct ; 
the  certainty  of  the  Intuition  is  improperly  extended  to  the 


AND   THE   CAUSES   OF  ERROR.  429 

Inference  which  is  drawn  from  it,  and  drawn  so  quickly 
and  easily  that  it  is  mistaken  for  a  part  of  the  observation 
itself.  When  Dr.  Cullen  remarked,  with  as  much  truth 
as  point,  that  "  there  are  more  false  facts  than  there  are 
false  theories  in  the  world,"  he  did  not  mean  to  impugn 
the  general  disposition  of  men  to  tell  the  truth.  He  al- 
luded to  what  are  generally  supposed  to  be  facts,  and 
which  go  by  that  name,  but  are  really  nothing  but  loose 
compounds  of  matters  of  opinion  with  those  of  observa- 
tion. Probably  what  he  had  in  mind  was  the  insufficiency 
of  the  evidence  on  which  the  members  of  his  own  profes- 
sion, that  of  Medicine,  are  often  obliged  to  act.  Thus,  it 
is  said  that  a  patient  is  in  a  Consumption  ;  this,  if  true, 
would  be  a  fact ;  but  the  only  known  fact  is,  that  certain 
symptoms  were  manifested  from  which  it  was  inferred, 
perhaps  wrongly,  that  the  case  was  one  of  Consumption. 
Again,  it  is  announced  as  a  fact,  that  the  use  of  a  certain 
medicine  cured  the  disease ;  when  the  truth  is,  that  the 
dose  was  administered,  and  the  man  got  well,  perhaps  in 
spite  of  the  medicine.  Men  are  so  prone  to  confound  their 
own  crude  conjectures  with  what  they  have  actually  seen 
or  heard,  that  very  few,  except  those  who  have  been  care- 
fully trained  to  scientific  habits  of  mind,  can  be  trusted  to 
report  their  own  observations,  until  they  have  undergone 
a  severe  cross-examination.  They  do  not  intend  to  de- 
ceive others,  but  they  have  effectually  deceived  them- 
selves. The  reputed  sciences  of  Phrenology  and  Animal 
Magnetism  rested  exclusively,  in  the  opinion  of  their  ad- 
mirers, on  a  basis  of  observed  facts,  and  hence  were  to  be 
maintained,  in  spite  of  the  arguments  with  which  they 
were  assailed,  because  facts  are  admitted  to  be  a  better 
test  of  truth  than  reasoning.  But  it  became  evident  on 
severe  scrutiny,  that  this  basis  was  made  up,  for  the  most 
part,  out  of  what  Dr.  Cullen  calls  "  false  facts." 

On  account  of  this  frequent  confusion  of  two  very  dis- 


430  THE  SOURCES   OF  EVIDENCE 

similar  things,  it  is  commonly  said,  and  with  good  reason, 
that  before  accepting  Testimony,  we  ought  to  have  satis- 
factory proof  both  of  the  veracity  and  the  competency  of 
the  witness.  But  if  people  generally  could  be  trusted  to 
separate  their  Inferences  from  their  observations,  and  to 
report  the  latter  unmixed,  it  would  evidently  be  enough 
to  have  assurance  only  upon  the  former  point.  In  respect 
only  to  their  quality  or  certainty,  though  not  with  regard 
to  their  extent  or  comprehensiveness,  one  man's  Intuitions 
are  as  good  as  another's.  The  one,  indeed,  may  see  more 
than  the  other,  because  he  knows  where  to  look  and  what 
to  observe.  He  will  therefore  have  more  to  report,  or,  at 
any  rate,  more  that  is  pertinent  and  useful.  But  the  Tes- 
timony of  the  other,  as  far  as  it  goes,  will  be  equally  valid 
and  trustworthy,  for  it  is  equally  a  report  of  what  has  actu- 
ally been  observed,  and  the  Intuitive  faculty  cannot  de- 
ceive. The  only  doubt,  then,  which  can  properly  affect 
the  reception  of  Testimony,  or  the  admission  of  other  peo- 
ple's experience  as  at  least  of  equal  value  with  our  own,  is 
that  which  regards  the  disposition  of  the  witness  to  tell  the 
truth.  Doubts  respecting  his  competency  as  an  observer 
can  be  settled  by  sifting  the  report  itself,  better  than  by 
inquiring  into  the  abilities  of  him  who  made  it. 

The  proper  distinction  to  be  made  is,  that  the  claims  of 
Testimony  to  be  accepted  depend  upon  the  evidence  which 
is  offered  as  to  the  Veracity  of  the  witness,  while  those  of 
Authority  rest  upon  the  proofs  which  we  possess  of  the 
Competency  of  the  person  whose  opinions  we  are  invited 
to  follow.  The  rules  for  forming  an  estimate  either  of  the 
Veracity  of  an  observer  or  the  Competency  of  a  judge  are 
too  obvious  to  need  mention  here,  except  in  very  general 
terms.  "In  regard  to  the  honesty  of  a  witness,"  says 
Esser,  as  translated  by  Hamilton,  "  this,  though  often 
admitting  of  the  highest  probability,  never  admits  of  abso- 
lute certainty ;  for  though,  in  many  cases,  we  may  know 


AND  THE   CAUSES   OF  ERROR.  431 

enough  of  the  general  character  of  the  witness  to  rely  with 
perfect  confidence  on  his  Veracity,  in  no  case  can  we  look 
into  the  heart,  and  observe  the  influence  which  motives 
have  actually  had  upon  his  volitions.  We  are,  however, 
compelled,  in  many  of  the  most  important  concerns  of  our 
existence,  to  depend  on  the  Testimony,  and  consequently 
to  confide  in  the  sincerity,  of  others.  But,  from  the  moral 
constitution  of  human  nature,  we  are  warranted  in  presum- 
ing on  the  honesty  of  a  witness ;  and  this  presumption  is 
enhanced  in  proportion  as  the  following  circumstances  con- 
cur in  its  confirmation.  In  the  first  place,  a  witness  is  pre- 
sumed to  be  veracious  in  this  case,  in  proportion  as  his  love 
«of  truth  is  already  established  from  others.  In  the  second 
place,  a  witness  is  to  be  presumed  veracious,  in  proportion 
as  he  has  fewer  and  weaker  motives  to  falsify  his  Testi- 
mony. In  the  third  place,  a  witness  is  to  be  presumed 
veracious,  in  proportion  to  the  likelihood  of  contradiction 
which  his  Testimony  would  encounter,  if  he  deviated  from 
the  truth." 

In  respect  to  the  Competency  of  the  person  to  whose 
Authority  we  are  requested  to  defer,  the  only  important 
principle  which  needs  to  be  here  laid  down  is  contained  in 
the  old  adage,  Cuique  credendum  est  in  sud  arte,  —  Trust 
each  person  in  his  own  specialty.  Eminence  in  one  depart- 
ment of  science,  far  from  being  an  indication  of  superior 
power  of  judgment  and  reasoning  in  other  departments, 
is  often  a  disqualification  for  forming  a  correct  opinion  in 
them.  The  mind  is  prone  to  carry  over  the  special  forms 
and  processes  which  are  appropriate  to  one  science  into 
others,  where  they  are  out  of  place,  and  lead  only  to  error. 
To  adopt  Bacon's  expressive  metaphor,  it  imports  into  a 
new  sphere  of  research  the  rust  and  tarnish  contracted  in 
the  workshop  wherein  it  has  chiefly  labored.  A  distin- 
guished mathematician,  other  things  being  equal,  is  not  so 
competent  to  form  an  opinion  upon  some  disputed  point  in 


432  THE  SOURCES  OF   EVIDENCE 

the  moral  sciences,  as  one  who  is  conversant  with  ques- 
tions of  this  sort,  though  he  has  never  gained  distinction 
in  them,  and  may  be  ignorant  of  the  first  principles  of 
Algebra  and  the  Calculus.  "  The  merit  of  a  mathemati- 
cal invention,"  as  Hamilton  justly  remarks,  "consists  in 
the  amount  of  thought  which  it  supersedes";  and  hence 
it  is  matter  of  common  remark,  that  those  who  are  most 
capable  of  making  such  inventions,  and  profiting  by  them, 
are  least  fitted  for  reasoning  by  Induction  and  Analogy. 
Consequently,  "  Mathematics  afford  us  no  assistance  either 
in  conquering  the  difficulties,  or  in  avoiding  the  dangers, 
which  we  encounter  in  the  great  field  of  probabilities 
wherein  we  live  and  move." 

Hume's  celebrated  argument  against  the  credibility  of 
miracles  is  a  fallacy  which  results  from  losing  sight  of  the 
distinction  between  Testimony  and  Authority,  between 
Veracity  and  Competency.  He  argues,  that  it  is  contrary 
to  all  experience  that  a  Law  of  Nature  should  be  broken, 
but  it  is  not  contrary  to  experience  that  human  testimony 
should  be  false  ;  and  therefore  we  ought  to  believe  that 
any  amount  of  Testimony  is  false,  in  preference  to  admit- 
ting the  occurrence  of  a  miracle,  as  this  would  be  a  viola- 
tion of  Law.  We  answer,  that  the  miraculous  character 
of  an  event  is  not  a  matter  of  Intuition,  but  of  Inference ; 
hence,  it  is  not  to  be  decided  by  Testimony,  but  by  Rea- 
soning from  the  probabilities  of  the  case,  the  only  question 
being  whether,  in  view  of  all  the  circumstances,  the  Con- 
clusion is  competent  that  the  occurrence  was  supernatural. 
The  Testimony  relates  only  to  the  happening  of  the  event 
considered  merely  as  an  external  phenomenon ;  the  ques- 
tion respecting  the  nature  of  this  event,  whether  it  is,  or  is 
not,  a  violation  of  Physical  Law,  whether  it  is  an  effect 
of  this  or  that  Efficient  Cause,  cannot  be  determined  by 
Intuition  and  Testimony,  but  is  a  matter  for  Judgment 
founded  on  Reasoning,  in  view  of  all  the  circumstances  of 


AND  THE   CAUSES   OF  ERROR.  433 

the  case.  If  doubtful  of  our  own  Competency  to  form  a 
correct  opinion  on  this  point,  we  may  defer  to  the  Author- 
ity of  another,  who  is  familiar  with  the  kind  of  Reasoning 
by  which  such  questions  are  settled.  Now  we  have  abun- 
dant evidence  from  experience,  that  no  event  whatever, 
regarded  simply  as  an  external  phenomenon,  can  be  so 
strange  and  marvellous  that  sufficient  Testimony  will  not 
convince  us  of  the  reality  of  its  occurrence.  To  the  con- 
temporaries of  our  Saviour,  not  even  bringing  a  dead  man 
to  life  would  have  appeared  so  incredible  as  the  transmis- 
sion of  a  written  message  five  thousand  miles,  without 
error,  within  a  minute  r*  time.  Yet  this  feat  has  been 
accomplished  by  the  Magn^ic  Telegraph.  Why  do  we 
decide,  then,  that  the  raising  of  Lazarus  was,  and  the 
transmission  of  intelligence  by  telegraph  is  not,  a  mira- 
cle? Evidently  not  by  Intuition,  but  by  reasoning  from 
the  very  different  circumstances  of  the  two  cases.  The 
fact,  that  the  eyes  of  the  blind  were  opened,  or  a  storm  was 
reduced  to  a  calm,  or  the  dead  were  raised,  is  established 
by  Intuition  and  Testimony,  which  have  established  many 
other  facts  quite  as  wonderral ;  the  character  of  this  fact, 
whether  miraculous  or  not,  is  to  be  settled  in  a  very  dif- 
ferent manner.  We  say,  then,  that  Hume's  argument, 
which  is  based  exclusively  upon  an  appeal  to  experience 
and  Testimony,  is  totally  inapplicable  to  the  question  re- 
specting the  credibility  of  a  miracle.  Testimony  has  noth- 
ing to  do  with  the  correct  inference  of  a  Conclusion  from 
its  Premises. 

We  can  touch  only  very  briefly  on  the  Criticism  of  re- 
corded Testimony,  and  of  writings  in  general.  As  we  must 
avail  ourselves,  in  the  construction  of  Science,  of  the  ex- 
perience of  former  generations,  in  respect  to  which  the 
Testimony  of  eye-  and  ear-witnesses  is  no  longer  directly 
accessible,  we  are  obliged  to  consider  the  credibility  of 
this  Testimony  as  affected  by  the  channels  of  transmission 

19  BB 


434  THE   SOURCES   OF  EVIDENCE 

through  which  it  has  been  passed.  There  are  but  two  such 
channels,  Tradition  and  Ancient  Writings.  The  former 
of  these  may  be  left  out  of  account ;  for  if  the  lapse  of  time 
has  been  considerable,  the  probability  that  the  Testimony, 
if  transmitted  merely  by  word  of  mouth,  has  been  mate- 
rially altered  or  falsified,  is  so  great,  that  the  report  can  be 
received  only  with  extreme  caution.  But  it  has  already 
been  mentioned,  that  the  invention  of  the  art  of  writing  has 
rendered  it  possible  for  the  experience  of  a  former  genera- 
tion to  be  handed  down,  through  an  indefinite  lapse  of  cen- 
turies, in  as  perfect  a  state  as  that  in  which  it  was  first 
communicated  to  those  who  were  the  contemporaries  of 
the  events  narrated.  This  is  possible,  we  say ;  the  ques- 
tion whether  it  has  been  actually  so  transmitted  is  what  we 
have  to  consider  in  the  Criticism  of  Ancient  Writings. 

When  a  document  purporting  to  be  the  recorded  Testi- 
mony of  certain  individuals  of  a  former  generation  is  pre- 
sented to  us,  we  have  first  to  inquire  whether  it  is  actually 
the  handwriting,  or  the  composition  as  taken  down  by  dic- 
tation, or  a  faithful  report,  made  at  the  time,  of  the  sub- 
stance of  the  evidence  of  the  individuals  whose  names  it 
bears,  or  to  whom  it  is  attributed.  The  establishment  of 
either  of  these  three  points  is  the  proof  of  what  is  called 
the  Genuineness  of  the  writing.  It  is  comparatively  un- 
important which  of  the  three  is  proved,  as  either  of  them 
gives  us  assurance  that  the  document  is  a  faithful  record 
of  the  Testimony  of  the  persons  whose  evidence  is  to  be 
weighed.  Thus,  even  if  we  were  sure  that  the  Testimony 
of  the  Evangelists  was  originally  written  out  by  their  own 
hands,  we  certainly  do  not  possess  their  autograph  copies ; 
still,  the  Gospels  are  Genuine,  if  we  have  sufficient  evi- 
dence that  they  are  faithful  records,  made  at  the  time,  (or 
correct  transcripts  of  such  records,)  of  what  the  Evange- 
lists said. 

But  a  second  question  must  be  answered  before  we  can 


AND  THE  CAUSES  OF  ERROR.  435 

accept  tlie  evidence  furnished  by  the  document.  "We  must 
be  satisfied,  not  only  that  the  Testimony  is  Genuine, — that 
it  was  actually  given  by  those  from  whom  it  purports  to 
come,  but  that  it  is  Authentic,  —  that  this  Testimony  is 
a  true  and  faithful  narrative  of  what  actually  happened. 
Proofs  of  the  Genuineness  of  the  writing  amount,  at  the 
utmost,  only  to  bringing  the  witnesses  into  court  and  estab- 
lishing their  identity ;  proofs  of  the  Authenticity  must  be 
found  by  sifting  their  evidence,  and  applying  to  it  all  the 
tests  and  means  of  verification  which  we  possess,  in  order 
to  ascertain  whether  they  are  telling  the  truth.  If  not 
Genuine,  the  document  is  said  to  be  Spurious;  if  not 
Authentic,  it  is  false. 

As  most  of  the  tests  and  proofs  of  the  Genuineness  and 
Authenticity  of  a  writing  are  such  as  readily  suggest  them- 
selves to  the  inquirer,  it  is  unnecessary  to  consider  them 
here  at  any  length.  Generally,  they  may  be  divided  into 
two  classes,  called  respectively  the  External  and  the  Inter- 
nal Evidences  of  the  point  to  be  proved.  The  External 
Evidences  of  Genuineness  are  to  be  found  either  in  other 
and  admitted  writings  of  the  supposed  author,  or  in  the 
works  of  writers  who  were  either  his  contemporaries,  or 
nearly  of  the  same  antiquity ;  and  the  evidence  is  either 
direct,  if  the  disputed  writing  is  therein  explicitly  attributed 
to  him,  or  indirect,  if  these  works  quote  as  his  production 
passages  which  are  found  in  the  document.  This  indirect 
testimony  has  the  greater  force,  for  on  account  of  its  casual 
or  incidental  character  there  is  less  reason  to  suspect  that  it 
has  been  forged.  The  External  Evidences  of  the  Authen- 
ticity of  the  writing,  considered  as  a  narrative  of  facts,  are 
too  numerous  to  mention.  They  are  found  in  allusions  to 
the  same  facts,  or  to  incidents  obviously  connected  with 
them,  by  contemporary  authors ;  in  customs,  traditions,  and 
institutions,  which  have  come  down  to  later  times,  and  the 
origin  of  which  cannot  be  accounted  for,  except  on  the  sup- 


436  THE   SOURCES    OF   EVIDENCE 

position  that  the  reported  events  actually  took  place ;  in 
coins,  medals,  and  inscriptions,  belonging  to  the  same  age, 
or  one  immediately  subsequent,  and  connected  by  equally 
close  relations  with  the  alleged  facts;  in  the  notoriety 
which  such  incidents  must  have  obtained,  the  interest  which 
must  have  been  felt  in  them,  and  the  consequent  probabil- 
ity that  falsifications  and  forgeries  respecting  them  would 
never  have  been  attempted,  or  would  have  been  detected 
and  disproved  at  the  time. 

Of  the  Internal  Evidence,  it  has  been  justly  remarked, 
that  it  is  weak  to  establish  either  Genuineness  or  Authen- 
ticity, but  powerful  to  disprove  both.  As  Hamilton  remarks, 
"  We  can  easily  conceive  that  an  able  and  learned  forger 
may  accommodate  his  fabrications  both  to  all  the  general 
circumstances  of  time,  place,  people,  and  language  under 
which  it  is  supposed  to  have  been  written,  and  even  to  all 
the  particular  circumstances  of  the  style,  habit  of  thought, 
personal  relations,  &c.  of  the  supposed  author."  On  the 
other  hand,  a  single  anachronism,  well  made  out,  in  respect 
either  to  events,  institutions,  customs,  or  even  the  use  of 
language,  is  as  fatal  to  the  document's  claim  to  antiquity,  as 
a  well-established  alibi  is  to  the  success  of  a  criminal  prose- 
cution. Bentley's  Dissertation  upon  the  Epistles  of  Phala- 
ris  might  have  been  limited  to  pointing  out  two  or  three  of 
the  numerous  anachronisms  which  he  detected  in  them,  if 
his  only  object  in  writing  it  had  been  to  prove  that  these 
alleged  Epistles  were  an  impudent  forgery.  In  respect  to 
the  Authenticity  of  a  narrative,  it  is  to  be  observed,  that 
the  credibility  of  certain  facts  is  one  thing,  and  the  proof 
of  their  actual  occurrence  is  another.  For  establishing  the 
former,  Internal  Evidence  is  sufficient ;  for  the  latter,  it  is 
powerless,  being  entirely  inapplicable.  By  saying  that  a 
narrative  of  certain  events  bears  with  it  Internal  Evidence 
of  its  truth,  we  mean  only  that  the  events  are  possible,  — 
that  they  are  consistent  with  each  other,  —  that  they  liar- 


AND  THE  CAUSES  OF  ERROR.  437 

monize  with  what  we  know  from  other  sources  concerning 
the  men  of  that  country  and  that  age,  —  that  they  are  con- 
formable to  the  ordinary  course  of  things.  All  this  may  be 
true  of  an  avowed  fiction.  Some  of  Shakespeare's  plays, 
most  of  Scott's  novels,  have  as  much  Internal  Evidence  of 
truth  as  any  testimony  given  in  a  court  of  justice.  They 
may  have  even  more  ;  for  it  is  a  common  proverb  that  truth 
is  often  stranger  than  fiction.  If  we  disregard  all  extrane- 
ous circumstances,  and  look  only  at  the  face  of  the  narrar 
tive,  Robinson  Crusoe  appears  as  true  a  story  as  Cook's 
Voyages,  and  Richardson  the  novelist  is  as  faithful  an  his- 
torian as  Hume. 

As  the  evidence  from  the  several  sources  that  have  now 
been  mentioned  may  be  of  various  degrees  of  strength,  and 
as  opinion  is  often  drawn  in  opposite  directions  by  conflict- 
ing testimony,  we  are  naturally  led  to  inquire  whether 
there  is  any  measure  of  probability,  or  any  means  of  accu- 
rately estimating  the  amount  of  belief  which  ought  to  be 
accorded  under  different  circumstances.  This  brings  us  at 
once  to  the  Theory  of  Probabilities,  or,  as  the  mathemati- 
cians sometimes  call  it,  the  Doctrine  of  Chances.  Only 
the  outlines,  or  first  principles,  of  the  subject  can  be  con- 
sidered here,  as  the  details  are  exclusively  mathematical, 
and  so  do  not  come  within  our  province. 

It  is  first  to  be  observed,  that,  in  the  calculation  ot 
Chances,  as  in  every  other  department  of  pure  mathe- 
matics, since  the  reasoning  employed  is  Demonstrative  in 
character,  the  correctness  of  the  results  obtained  depends 
upon  the  truth  of  certain  assumptions  made  in  the  outset ; 
and  the  applicability  of  one  of  these  results  to  any  given 
case,  or  actual  instance,  turns  upon  the  answer  to  the  ques- 
tion whether  this  instance  is  exactly  comprehended  within 
the  Definition  of  the  Concept  upon  which  the  whole  calcu- 
lation is  based.  Thus,  in  calculating  the  probability  of  any 
one  out  of  a  given  number  of  events,  it  is  assumed  that  all 


438  THE  SOURCES   OF  EVIDENCE 

the  events  considered  are  equally  possible,  —  that  no  one 
has  any  advantage  which  would  render  it  more  likely  to 
happen  than  the  others.  Practically,  this  supposition  is 
never  fulfilled.  In  illustrating  their  conclusions,  the  mathe- 
maticians have  shown  much  ingenuity  in  selecting  cases 
where  the  chances  would  seem  to  be  equally  balanced ;  but 
it  is  easy  to  show  that  they  have  never  entirely  succeeded. 
Their  favorite  case  is  that  of  putting  a  number  of  balls, 
equal  in  size,  but  different  in  color,  into  an  urn,  and  then 
considering  the  probability  of  a  blindfolded  person  drawing 
one  of  a  certain  color  after  a  given  number  of  trials.  But 
suppose  the  number  of  balls  is  considerable,  that  all  the 
white  ones  are  first  thrown  in  together,  and  then  all  the 
black  ones ;  in  such  case,  the  chance  of  drawing  a  black 
ball  at  the  first  trial  is  obviously  much  greater  than  that  of 
a  white  one.  A  dozen  other  suppositions  might  be  made, 
depending  on  the  size  and  shape  of  the  urn,  and  the  manner 
of  throwing  in  the  balls,  any  one  of  which  would  be  fatal  to 
a  precise  agreement  of  the  actual  with  the  calculated  result. 
Another  favorite  case  is  that  of  throwing  up  a  half-penny, 
to  determine  whether  it  will  give  head  or  tail ;  but  here  it 
is  assumed  that  the  two  sides  of  the  coin  just  balance  each 
other,  which,  on  account  of  the  different  imprints  that  they 
bear,  is  never  the  case.  Even  in  the  better  chosen  illus- 
trations, then,  the  calculated  result  will  be  only  an  approx- 
imation to  the  truth.  In  ordinary  cases  in  which  the  Doc- 
trine of  Chances  is  applied,  as  in  gambling,  it  will  be  but  a 
rude  approximation ;  most  of  what  are  called  games  of 
chance  are,  at  least  in  some  faint  degree,  games  of  skill ; 
and  in  the  long  run,  though  not  necessarily  in  a  few  trials, 
skill  will  tell. 

In  most  cases  of  the  practical  application  of  the  Doctrine 
of  Chances,  the  existence  of  numerous  causes  of  error  is 
admitted ;  but  as  we  know  nothing  of  the  character  of  these 
causes,  and  do  not  see  any  reason  why  more  of  them  should 


AND  THE  CAUSES  OF  ERROR.  439 

operate  on  one  side  than  on  the  other,  it  is  assumed  that,  in 
the  long  run,  they  will  compensate  each  other,  so  that  the 
result  will  agree  with  the  calculation.  But  this  is  only  the 
argument  ad  ignorantiam,  the  fallacy  of  which  has  already 
been  noticed ;  because  we  do  not  know  any  reason  why  there 
should  not  be  as  many  and  as  heavy  errors  on  one  side  as 
on  the  other,  it  does  not  follow  that  there  is  no  such  rea- 
son. It  was  for  a  long  time  supposed,  that  the  arithmetical 
mean  of  several  distinct  observations  of  the  same  astrono- 
mical phenomenon  would  afford  the  nearest  approximation 
to  a  correct  result,  as  there  was  no  known  reason  why  dif- 
ferent observers  should  not  err  as  much  on  one  side  as  on 
the  other.  But  it  is  now  known  that  each  observer  has  a 
constant  tendency,  distinctly  appreciable  in  amount,  to  err 
in  one  direction ;  and  if  allowance  is  not  made  for  this 
"  personal  equation,"  as  it  is  called,  the  arithmetical  mean 
is  not  the  nearest  attainable  approximation  to  the  truth. 

What  is  called  "  the  Method  of  Least  Squares  "  has  been 
adopted  as  a  mode  of  finding  the  most  probable  result  in 
those  cases  in  which  the  arithmetical  mean  is  not  an  applica- 
ble expedient  for  determining  this  probability.  This  Method 
proceeds  upon  the  assumption  that  all  errors  are  not  equally 
probable,  but  that  small  errors  are  more  probable  than  large 
ones.  An  easy  corollary  from  this  assumption  is,  that  the 
most  probable  conclusion  can  be  obtained  by  making,  not 
the  errors  themselves,  but  the  sum  of  the  squares  of  these 
errors,  of  the  smallest  possible  amount.  To  borrow  an  in- 
stance from  Dr.  Whewell :  —  Let  the  observed  numbers  be 
4,  12,  14 ;  and  suppose  it  known  that  these  numbers  must 
be  erroneous,  as  they  ought  to  form  an  arithmetical  pro- 
gression. The  question  is,  what  arithmetical  progression 
do  they  most  probably  represent.  The  following  table 
shows  that  there  are  three  such  progressions  which  approx- 
imate the  observed  series,  and  also  indicates  which  one  of 
them,  according  to  the  Method  of  Least  Squares,  is  the 
most  probable. 


440  THE  SOURCES   OF   EVIDENCE 


Observed  Series    4,  12,  14 

Errors. 

Sums  of 
errors. 

Sums  of  squares 
of  errors. 

1st  Progression      4,     9,  14 
2d           "                6,  10,  14 

0,  3,  0 
2,  2,  0 

3 
4 

9 
8 

3d           "               5,  10,  15 

1,  2,  1 

4 

6 

We  here  see,  although  the  first  progression  gives  the 
least  sum  of  errors,  the  third  shows  the  least  sum  of  the 
squares  of  the  errors ;  and  therefore,  according  to  this 
Method,  the  third  is  the  most  probable  of  the  three. 

These  remarks  were  necessary  in  order  to  obviate  the 
inference  which  too  many  are  inclined  to  draw,  that,  be- 
cause the  calculations  in  the  Doctrine  of  Chances  are  made 
on  strict  mathematical  principles,  the  calculated  probability 
of  an  event,  in  any  actual  application  of  this  Doctrine, 
must  therefore  be  mathematically  exact  and  absolutely 
certain.  On  the  contrary,  in  any  such  application  of  the 
principles,  the  result  is  only  a  rough  approximation  to  the 
truth. 

It  is  also  important  to  remember,  that  the  application  of 
the  Theory  of  Probabilities  only  shows  us  what  we  ought 
to  expect,  or  what,  as  rational  beings,  we  are  bound  to  be- 
lieve, and  does  not  reveal  any  Cause  or  Law  that  actually 
determines  the  occurrence.  To  speak  technically,  the  cal- 
culated probability  is  subjective,  and  not  objective ;  it  re- 
veals what  may  be  called  a  law  of  thought,  but  not  a  law 
of  things.  "  The  subject-matter  of  calculations  in  the 
Theory  of  Probabilities,"  says  Professor  Donkin,  u  is  quan- 
tity of  belief.  In  every  problem,  a  certain  number  of  hy- 
potheses are  presented  to  the  mind,  along  with  a  certain 
quantity  of  information  relating  to  them;  the  question  is, — 
In  what  way  ought  belief  to  be  distributed  among  them  ?  " 
The  calculation  of  the  chances  does  not  assume  to  increase 
this  "  quantity  of  information,"  or  to  reveal  any  new  data 
on  which  our  judgntent  ought  to  be  based ;  but  only  how 
we  ought  to  judge  and  to  act  on  the  data  that  we  already 


AND  THE  CAUSES  OF  ERROR.  441 

possess.  The  doctrine  does  not  even  assure  us  that  the 
calculated  result  will  be  verified  at  the  first  trial,  or  at  any 
subsequent  trial ;  but  it  only  shows  us  how  we  ought  to 
expect  the  actual  results  to  be  distributed  in  the  course  of 
an  infinite  number  of  trials.  The  calculation  does  not  re- 
late merely  to  future  events,  the  occurrence  of  which  is 
still  contingent ;  it  may  be  applied  also  to  the  past,  to  de- 
termine the  probability  that  the  event  did,  or  did  not,  take 
place.  In  cases  of  the  latter  sort,  it  is  sufficiently  obvious 
that  the  application  of  the  Theory  of  Probabilities  does  not 
in  any  wise  affect  the  event  itself,  which  is  already  irrev 
ocably  determined  either  one  way  or  the  other ;  but  only 
assumes,  in  our  ignorance  of  what  the  actual  result  has 
been,  to  determine  what  we  ought  to  believe  respecting  it. 

Keeping  this  distinction  in  mind,  we  can  explain  the 
seeming  paradox,  that  an  event  should  be  sure  to  happen 
at  the  first  trial,  though  the  chances  were  indefinitely  great 
against  its  occurrence.  Put  into  an  urn  any  number  of 
balls  numbered  consecutively  from  one  upwards,  —  say 
1,000.  Of  course,  there  are  999  chances  to  1  against  a 
blindfolded  person  drawing,  at  the  first  trial,  the  particular 
ball  marked  with  any  one  of  these  numbers ;  and  yet  some 
one  ball  so  marked  must  be  drawn.  But  this  is  no  viola- 
tion of  the  law  regulating  what  we  ought  to  expect ;  for 
we  ought  not  to  expect  any  particular  number  to  come  at 
the  first  trial,  though  we  are  certain  that  some  —  we  know 
not  what  —  number  must  so  come. 

It  is  assumed  in  the  Doctrine  of  Chances,  that  the  va- 
rious degrees  of  belief  may  be  represented  by  numbers. 
An  impossible  event,  as  it  has  no  probability  whatever  in 
its  favor,  is  appropriately  represented  by  zero.  An  event 
which  is  sure  to  happen,  as  the  expectation  of  its  occur- 
rence is  not  broken  or  divided  by  any  chance  of  failure, 
might  be  represented  by  any  integral  number;  its  most 
convenient,  because  the  simplest,  symbol  is  unity.     Then 

19* 


442  THE   SOURCES   OF  EVIDENCE 

al]  the  degrees  of  probability  between  impossibilit}*-  and 
certainty  will  be  denoted  by  the  fractions  that  may  be  in- 
terpolated between  0  and  1. 

The  first  principle  of  the  Doctrine  of  Chances  is,  that 
the  'probability  of  an  uncertain  event  is  represented  by  the 
number  of  chances  favorable  to  its  occurrence,  divided  by  the 
total  number  of  chances  whether  favorable  or  unfavorable. 
Thus,  as  a  pack  contains  52  cards,  divided  into  four  equal 
suits,  into  12  pictured  and  40  plain  cards,  and  into  26  red 
and  26  black  cards,  the  chance  of  drawing  a  heart  at  the 
first  trial  is  ^|  or  \  ;  of  a  pictured  card,  ^|  or  -fy  ;  of  a  red 
card,  II  or  J.  This  last  case  represents  an  event  which  is 
entirely  uncertain,  the  chances  being  equal  for  and  against 
its  occurrence.  We  may  get  rid  of  the  fractional  form  by 
expressing  the  probability  of  an  event  in  that  mode  which 
is  called  "  the  odds  "  ;  that  is,  we  may  take  the  numerator 
to  express  the  chances  for,  and  the  difference  between  the 
numerator  and  the  denominator  to  signify  the  chances 
against,  the  occurrence.  This  rule  is  an  immediate  corol- 
lary from  the  first  principle  as  just  stated,  since  the  numer- 
ator gives  the  number  of  favorable  chances,  and  the  de- 
nominator the  total  number  of  them  both  favorable  and 
unfavorable.  Thus,  the  chance  of  drawing  a  pictured  card 
is  represented  fractionally,  as  above,  by  ^-,  or  by  the  odds 
as  3  to  10 ;  of  a  red  card,  as  f  f ,  or  26  to  26,  —  even 
chance. 

The  improbability  of  an  occurrence  is  denoted  by  the 
complement  of  the  fraction  which  expresses  its  probability  ; 
that  is,  the  odds  are  reversed.  Thus,  as  there  are  six  faces 
to  a  die,  all  of  which  are  supposed  to  be  equally  likely  to 
come  uppermost,  the  probability  of  throwing  six  is  J  or  1 
to  5 ;  the  improbability  of  it  is  1  —  J  =  |,  or  5  to  1.  The 
reason  of  this  rule  is  obvious;  the  improbability  of  one 
event  must  be  the  sum  of  the  probabilities  of  all  the  other 
possible  occurrences ;  and  as  the  total  of  all  the  chances. 


AND  THE  CAUSES  OF  ERROR.  443 

which  represents  what  is  sure  to  happen,  is  unity,  the  sum 
of  the  probabilities  of  all  the  others  is  found  by  subtract- 
ing the  probability  of  this  one  from  unity.  Thus,  some 
one  of  the  six  faces  must  come  uppermost ;  this  certainty 
is  denoted  as  1.  Then,  as  the  probability  of  a  six  is  J,  the 
chance  of  some  one  out  of  the  other  five  faces,  (in  other 
words,  the  improbability  of  a  six,)  is  1  —  J  =  J .  As  each 
of  the  five  other  faces  has  a  probability  of  J,  the  sum  of 
their  chances,  or  the  improbability  of  the  remaining  one,  is 
evidently  J. 

The  probability  of  a  compound  event  —  that  is,  of  two 
independent  uncertainties  happening  conjointly  —  is  ascer- 
tained by  multiplying'  the  separate  chances  of  the  two  to- 
g-ether. Thus,  the  chance  of  throwing  six  with  one  die 
being  J,  and  of  throwing  the  same  with  another  die  being 
^,  the  chance  of  obtaining  sixes  at  once  with  the  two  dice 
is  1  X  -J  =  g1^ .  This  rule,  again,  is  a  direct  corollary  from 
the  first  principle  as  already  enounced ;  for  as  the  number 
of  possible  throws  with  two  dice  is  6  X  6  =  36,  (since 
each  face  of  the  one  might  be  combined  with  either  of  the 
six  faces  of  the  other,)  and  as  only  one  of  these  is  favor- 
able, the  odds  are  evidently  as  1  to  35.  To  take  another 
instance :  —  the  chance  of  drawing  a  pictured  card  out  of 
a  pack  being  ^-,  and  of  a  red  card,  J,  the  probability  of 
having  a  red  pictured  card  is  ^  X  \  =  ^  or  -^,  as  there 
are  six  red  pictured  cards  out  of  the  52  in  the  pack. 

According  to  this  rule,  the  chance  of  drawing  a  red  card 
four  times  in  succession,  the  card  being  replaced  after  each 
trial,  so  that  the  number  in  the  pack  shall  always  be  52, 
will  beJx£X£x£  =  iV>  or  only  1  to  15.  But  gam- 
blers often  deceive  themselves  in  respect  to  the  application 
of  this  rule.  As  it  is  so  unlikely  that  a  red  card  will  turn 
up  several  times  in  succession,  they  imagine  that,  after  it 
has  thrice  thus  turned  up,  the  chance  of  obtaining  a  black 
card  at  the  fourth  trial  is  much  greater  than  it  was  at  first. 


444  THE   SOURCES   OF  EVIDENCE 

But  it  is  not  so ;  if  the  card  drawn  is  always  immediately 
replaced,  the  probability  of  drawing  a  black  card  after  Ave 
have  drawn  a  red  one  at  three,  or  even  at  a  thousand,  suc- 
cessive trials,  is  precisely  what  it  was  before  the  first  ex- 
periment, —  namely,  J.  The  number  of  cards  being  always 
the  same,  26  red  and  26  black,  the  probability  of  obtaining 
a  red  one  is  always  the  same,  whatever  previous  experiments 
may  have  been  made  with  the  same  pack.  The  three  ex- 
periments already  tried  have  reduced  so  many  uncertainties 
to  certainties,  —  that  is,  have  thrown  them  out  of  the  cal- 
culation in  the  Doctrine  of  Chances,  which  deals  only  with 
uncertain  events.  Before  any  trial  was  made,  the  chance 
of  a  red  card  turning  up  four  times  in  succession  was  only 
-j5^,  each  of  the  four  results  being  then  uncertain ;  after 
three  trials,  but  one  event  is  still  an  uncertainty,  and  the 
probability  of  its  occurrence  is  J.  "We  see,  then,  the  folly 
of  the  gambler's  expectation  that  his  luck  must  soon  turn, 
because  he  has  had  a  long  series  of  ill-luck.  But  all  his 
past  trials  having  been  reduced  to  certainties,  his  chance 
of  good  fortune  is  now  precisely  what  it  was  when  he  be- 
gan. His  only  chance  of  success,  after  he  has  had  a  long 
series  of  misfortunes,  is  to  stop  playing  altogether;  and  this 
is  also  the  best  thing  he  can  do,  if  fortune  has  smiled  upon 
him. 

The  development  of  these  principles  must  be  left  to  the 
mathematician ;  but  a  further  caution  in  respect  to  the 
application  to  be  made  of  them  by  the  gambler  may  be 
borrowed  from  Buffon.  "  If  two  men,"  he  asks,  "  were  to 
determine  to  play  for  their  whole  property,  what  would  be 
the  effect  of  this  agreement  ?  The  one  would  only  double 
his  fortune,  and  the  other  reduce  his  to  naught.  What 
proportion  is  there  between  the  loss  and  the  gain  ?  The 
same  that  there  is  between  all  and  nothing.  The  gain  of 
the  one  is  but  a  moderate  sum ;  the  loss  of  the  other  is 
numeiically  infinite,  and  morally  so  great  that  the  labor  of 


AND   THE   CAUSES   OF  ERROR.  445 

his  whole  life  may  not,  perhaps,  suffice  to  restore  his  prop- 
erty." But  the  fascination  of  gambling  is  so  great,  and 
the  habit  of  it,  when  once  formed,  is  so  incontrollable,  that 
every  one  who  even  begins  to  play  may  be  regarded  as 
staking  his  whole  fortune  upon  the  issue,  and  thus  as  volun- 
tarily subjecting  himself  to  these  tremendous  odds. 

The  principal  intellectual  Causes  of  Error  have  been  al- 
ready indirectly  considered,  inasmuch  as  they  consist  in  any 
violation  of  the  rules  and  methods  which  have  been  laid 
down  for  the  attainment  of  truth.  But  the  moral  Causes 
which  blind  our  perceptions,  warp  our  judgments,  and  lead 
us  to  accept  illusions  in  the  place  of  truths,  deserve  some 
separate  notice.  Most  of  these  are  modifications  or  conse- 
quences of  self-love,  or  rather  of  that  short-sighted  selfish- 
ness which  has  more  regard  for  present  ease  and  enjoyment, 
however  trifling,  than  for  future  good,  however  great,  if 
the  latter  be  attainable  only  by  effort  and  self-denial.  Such 
are  prejudices,  pride,  undue  desires,  precipitancy,  and  sloth. 
All  of  these  are  faults  of  character  rather  than  of  intellect ; 
yet  they  are  more  frequent  sources  of  delusion,  and  more 
formidable  obstacles  to  our  mental  progress,  than  can  be 
found  in  the  original  weakness  and  limited  range  of  our 
faculties,  or  in  the  insufficiency  of  the  aids  and  incitements 
which  nature  furnishes  for  the  pursuit  of  truth.  We  ap- 
proach the  study  of  a  subject,  not  as  prepared  to  accept  any 
conclusions  to  which  our  researches  might  naturally  lead, 
but  with  minds  stuffed  with  preconceived  opinions,  which 
pride  prevents  us  from  relinquishing  after  they  have  been 
once  avowed,  or  with  a  bias  in  favor  of  some  startling  con- 
sequences of  the  inquiry,  the  announcement  of  which  may 
feed  our  vanity  or  establish  our  reputation.  Pride  also 
leads  us  astray,  by  inducing  us  to  over-estimate  the  extent 
and  importance  of  the  acquisitions  that  we  have  already 
made,  or  to  adopt  too  easily  the  conclusion  that  the  investi- 
gation has  reached  its  limit,  and  that  we  already  know  as 


446  THE   SOURCES   OF  EVIDENCE 

much  as  is  capable  of  being  known.  I  know  of  no  error 
which  is  more  fatal  to  progress  than  the  idea  that  there  is 
no  progress  to  be  made,  —  of  no  opinion  which  is  more  det- 
rimental to  improvement  than  the  belief  that  no  improve- 
ment is  possible.  It  is  true  that  a  low  estimate  of  the  ex- 
tent of  our  knowledge  does  not  amount  to  the  Christian 
virtue  of  humility  in  the  largest  sense.  It  may  be,  it  fre- 
quently is,  accompanied  with  a  very  lofty  opinion  of  the 
extent  of  our  powers,  or  the  excellence  of  our  natural  en- 
dowments. But  a  conceit  of  ability,  bad  as  it  is,  is  not  so 
injurious  to  progress  as  a  conceit  of  knowledge.  The  one 
encourages  a  person  to  study,  by  leading  him  to  believe  that 
he  can  grapple  with  any  subject ;  the  other  disposes  him  to 
sit  down  in  idleness,  under  the  belief  that  he  has  already 
mastered  that  subject.  Seneca  says,  Multos  potuisse  ad 
sapientiam  pervenire,  nisi  putassent  se  pervenisse,  —  Many 
might  have  obtained  wisdom,  if  they  had  not  supposed  that 
they  had  already  got  it. 

Moderation  in  our  personal  desires,  and  that  earnestness 
of  inquiring  purpose  which  leads  not  so  much  to  an  abne- 
gation as  to  the  entire  forgetfulness  of  self,  are  more  im- 
portant elements  of  success  in  the  pursuit  of  truth  than  is 
commonly  supposed.  The  brilliant  results  of  Dr.  Frank- 
lin's scientific  career  seem  attributable,  in  a  great  degree, 
to  his  generous  disregard  of  his  own  fame  and  standing  in 
the  eyes  of  the  public.  A  lively  curiosity,  an  eye  quick  at 
observation,  great  sagacity  in  detecting  the  more  occult  re- 
lations of  facts  and  bearings  of  experiments,  and  a  mind  of 
incessant  and  intense  activity,  were  not  the  only  means 
that  enabled  him  to  accomplish  so  much  in  science.  His 
attention  was  not  diverted  from  the  object  of  investigation 
by  any  regard  for  what  the  world  might  think  of  the  im- 
portance of  that  object,  or  of  his  own  merit  in  obtaining  it. 
The.  m  cessary  experiments  were  instituted,  not  to  convince 
others,  but  to  satisfy  himself.     The  most  brilliant  results  at 


ANE  THE  CAUSES  OF  ERROR.  447 

which  he  arrived  were  communicated  only  in  private  let- 
ters to  a  few  friends,  to  whom  he  left  the  care  of  publishing 
them  or  not,  as  they  saw  fit.  His  theories  sat  loosely  upon 
him,  and  he  modified  or  abandoned  them,  when  further  ob- 
servations made  it  necessary,  without  dreading  the  charge 
of  inconsistency,  and  without  shame  at  confessing  a  mis- 
take. He  was  never  seduced,  by  the  accidental  brilliancy 
or  novelty  of  one  object  of  inquiry,  to  pay  more  attention 
to  it  than  to  another,  apparently  of  a  more  homely  charac- 
ter, but  really  of  equal  interest  to  a  philosophical  mind. 
He  studied  the  means  of  remedying  smoky  chimneys  with 
as  much  ardor  and  industry  as  he  showed  in  penetrating 
the  secrets  of  the  clouds,  and  robbing  the  thunderbolt  of  its 
terrors.  He  formed  theories  of  the  earth,  and  projects  for 
cleaning  and  lighting  the  streets  of  Philadelphia,  with  equal 
zeal ;  and  having  communicated  the  former  in  a  private 
letter  to  a  friend,  and  urged  upon  his  fellow-citizens  the 
adoption  of  the  latter,  he  dismissed  both  from  his  mind,  and 
pursued  with  fresh  interest  a  wholly  different  set  of  inves- 
tigations. 

The  most  frequent  cause  of  failure  in  any  pursuit  is  the 
lack  of  earnestness.  Habit  may  impart  a  kind  of  mechan- 
ical facility  in  the  performance  of  a  given  task ;  but  there 
will  be  little  vigor  or  energy  in  the  work,  if  the  feelings 
be  not  deeply  interested  in  it,  so  that  the  result  shall  be 
awaited  with  eager  expectation  or  trembling  anxiety.  Long- 
continued  labor  easily  degenerates  into  mere  routine  ;  and 
then,  even  though  the  specific  object  in  view  should  be  ol>- 
tained,  —  though  a  science  should  be  learned  or  a  liveli- 
hood got,  —  there  will  be  no  strain  of  the  faculties,  and 
consequently  no  development  of  them,  —  no  correction  of 
errors,  and  therefore  no  discipline  of  mind.  This  is  the 
secret  of  the  great  force  displayed,  and  the  large  results 
that  are  often  accomplished,  by  those  who  are  opprobri- 
ously  termed  "men  of  one  idea,"  —  persons  who  have  con- 


448  THE   SOURCES   OF  EVIDENCE 

cent  rated  their  attention  upon  one  object,  and  who  pursue 
it,  regardless  of  everything  else,  with  all  the  strength  and 
the  bitterness  of  fanaticism.  Half  an  hour  of  strenuous 
exertion  is  worth  a  week  of  mechanical  and  desultory  la- 
bor. Too  often  we  dawdle  over  the  business  of  life,  instead 
of  taking  it  up  with  eagerness,  and  prosecuting  it  to  the  end 
as  a  work  of  love.  There  is  all  the  difference  in  the  world 
between  an  active  mind  and  a  passive  one  ;  between  ear- 
nestly hunting  after  truth,  and  only  swallowing  knowledge 
inertly,  as  it  is  poured  into  the  memory  by  a  teacher  or  a 
book,  and  just  as  quickly  washed  out  again.  We  are  made 
what  we  are,  experts  or  dolts,  much  more  by  our  acquired 
habits  than  by  success  or  failure,  in  the  attainment  of  knowl- 
edge. Aim  not  so  much  to  be  learned,  as  to  be  able  to 
learn ;  one  truly  wise  man  is  worth  a  hundred  erudite  ped- 
ants. The  study  of  Logic  itself  will  do  little  to  cultivate 
our  power  of  reasoning,  or  to  improve  our  habits  of  thought, 
except  indirectly,  by  the  effort  which  is  necessary  for  the 
mastery  of  its  principles,  and  by  the  endeavor  to  verify  or 
correct  them  in  the  course  of  our  subsequent  researches. 
"What  we  really  need  to  attain  is  Logical  power,  and  a 
knowledge  of  the  science  of  Logic  is  useful  so  far  only 
as  it  is  conducive  to  such  attainment. 

Among  the  occasions  for  the  use  of  this  power,  that  to 
which  the  gravest  responsibility  is  attached  is  the  formation 
of  our  opinions.  Properly  speaking,  we  must  all  begin  life 
without  any  opinions  which  we  can  call  our  own  by  any 
better  right  than  that  of  passive  inheritance  or  unconscious 
inoculation.  We  have  probably  imbibed  most  of  them  just 
as  we  took  the  measles  or  the  whooping-cough  in  infancy, 
from  accidental  contact  with  others.  We  are  Whig,  Dem- 
ocrat, or  Republican,  conservative  or  radical,  —  we  go  to 
the  Episcopal,  Presbyterian,  or  Congregationalist  church, — 
simply  because  parents  and  friends  thought  so,  or  did  so, 
formerly.     Now,  in  one  respect,  this  is  all  right  and  just  as 


AND   THE   CAUSES   OF  ERROR.  449 

it  should  be.  It  is  fortunate,  both  for  ourselves  and  the 
world,  that  we  begin  life  with  a  set  of  provisional  opinions 
already  formed,  not  by  us,  but  for  us.  This  vis  inertice  of 
opinion,  this  tendency  of  the  human  mind  to  move  in  the 
ruts  where  others  have  preceded  it,  is  the  great  conserva- 
tive principle  of  society,  all  that  keeps  us  from  intellectual 
and  social  anarchy.  Without  it,  all  the  wise  men  who 
have  been  before  us  would  have  lived  in  vain,  and  society 
would  drift  along  helplessly,  without  keel  or  rudder.  If 
we  were  not  willing  to  accept  opinions  before  we  are  able 
to  form  them  for  ourselves,  —  ay,  and  to  cling  to  them 
with  the  fondness  which  early  association  imparts,  —  half  of 
the  time  we  should  act  at  random,  and  the  other  half  ex- 
travagantly and  foolishly. 

But  we  cannot  pass  through  life  merely  as  docile  chil- 
dren; and  our  first  duty  as  men — at  any  rate,  as  educated 
and  thinking  men  —  is  to  begin  the  great  work  of  fashion- 
ing our  own  creeds  in  politics,  religion,  philosophy,  and  so- 
cial economy.  When  we  have  attained  our  majority,  we 
have  become  as  accountable  for  our  opinions  as  for  our  con- 
duct. A  wise  man,  however,  might  hesitate  before  going 
as  far  as  Descartes,  who  urges  us  to  begin  by  doubting 
everything ;  his  advice  is,  to  take  up  every  question,  as  it 
were,  de  novo,  with  a  determination  not  to  accept  any  an- 
swer to  it  the  correctness  of  which  is  not  made  out  by  evi- 
dence satisfactory  to  our  own  minds,  and  elicited  by  our  own 
inquiries.  A  safer  course,  as  it  seems  to  me,  is  to  begin, 
not  by  discarding  all  our  previous  opinions,  but  by  examin- 
ing the  foundations  on  which  they  rest.  There  is  just  as 
much  of  prejudice  and  rashness  in  presuming  that  they  are 
all  false,  as  in  believing,  previous  to  inquiry,  that  they  are 
all  true.  Do  not  ask,  Why  may  it  not  be  otherwise  ?  but 
rather,  Why  is  it  so  ?  The  presumption  is  in  favor  of  the 
received  doctrines  in  any  science,  until  good  reasons  are 
made  to  appear  for  doubting  or  denying  them.     But  the 

CO 


450        SOURCES   OF  EVIDENCE   AND   CAUSES   OF  ERROR. 

duty  of  inquiry,  in  order  to  ascertain  whether  there  are 
such  reasons,  is  one  which  always  exists,  and  which  opens 
the  largest  and  fairest  field  for  the  exercise  and  develop- 
ment of  our  powers  of  thought.  Only  by  such  exercise 
can  we  hope  to  perfect  our  knowledge  of  the  principles  of 
Logic,  and  to  make  that  knowledge  of  use  to  ourselves  and 
others.  "  We  employ  reason,"  said  the  Port-Royalist  logi- 
cians, "  as  an  instrument  for  acquiring  the  sciences,  whereas 
we  ought  to  use  the  sciences  as  a  means  of  perfecting  our 
reason,  correctness  of  judgment  and  accuracy  of  thought 
being  infinitely  more  valuable  than  all  the  speculative 
knowledge  which  we  can  obtain  from  the  best-established 
sciences.  Wise  men,  therefore,  ought  to  engage  in  the 
study  of  the  sciences  only  -so  far  as  they  conduce  to  this 
end,  and  to  make  them  only  the  training-ground,  and 
not  the  field  for  the  regular  employment,  of  their  mental 
powers." 


THE  END. 


«.  ON  THE  LAST  DATE 
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XS»?rS"5-  •*■ DAY 

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OVERDUE. 


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LD  21-10°m 


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